task_id stringlengths 23 52 | subset stringclasses 1
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values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-rlve-construct-hack-interval-l2-s6 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 45570 (that is, 10 * 4557) such that
f(L) + f(L+1) + ... + f(R) is divisible by 4557.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 4557, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 13, "R": 440} | 1 |
construct-rlve-construct-hack-interval-l2-s7 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 24980 (that is, 10 * 2498) such that
f(L) + f(L+1) + ... + f(R) is divisible by 2498.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 2498, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 23, "R": 273} | 1 |
construct-rlve-construct-hack-interval-l2-s8 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 21090 (that is, 10 * 2109) such that
f(L) + f(L+1) + ... + f(R) is divisible by 2109.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 2109, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 228} | 1 |
construct-rlve-construct-hack-interval-l2-s9 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 13650 (that is, 10 * 1365) such that
f(L) + f(L+1) + ... + f(R) is divisible by 1365.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 1365, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 1, "R": 158} | 1 |
construct-rlve-construct-hack-interval-l3-s0 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 7224040 (that is, 10 * 722404) such that
f(L) + f(L+1) + ... + f(R) is divisible by 722404.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 722404, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 19, "R": 37726} | 1 |
construct-rlve-construct-hack-interval-l3-s1 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 7777900 (that is, 10 * 777790) such that
f(L) + f(L+1) + ... + f(R) is divisible by 777790.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 777790, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 27, "R": 39934} | 1 |
construct-rlve-construct-hack-interval-l3-s2 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8460550 (that is, 10 * 846055) such that
f(L) + f(L+1) + ... + f(R) is divisible by 846055.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 846055, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 10, "R": 43579} | 1 |
construct-rlve-construct-hack-interval-l3-s3 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8234640 (that is, 10 * 823464) such that
f(L) + f(L+1) + ... + f(R) is divisible by 823464.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 823464, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 11, "R": 42454} | 1 |
construct-rlve-construct-hack-interval-l3-s4 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 4668990 (that is, 10 * 466899) such that
f(L) + f(L+1) + ... + f(R) is divisible by 466899.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 466899, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 25523} | 1 |
construct-rlve-construct-hack-interval-l3-s5 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 6255290 (that is, 10 * 625529) such that
f(L) + f(L+1) + ... + f(R) is divisible by 625529.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 625529, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 11, "R": 33198} | 1 |
construct-rlve-construct-hack-interval-l3-s6 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 6745030 (that is, 10 * 674503) such that
f(L) + f(L+1) + ... + f(R) is divisible by 674503.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 674503, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 52, "R": 35632} | 1 |
construct-rlve-construct-hack-interval-l3-s7 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 6142170 (that is, 10 * 614217) such that
f(L) + f(L+1) + ... + f(R) is divisible by 614217.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 614217, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 32619} | 1 |
construct-rlve-construct-hack-interval-l3-s8 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8409670 (that is, 10 * 840967) such that
f(L) + f(L+1) + ... + f(R) is divisible by 840967.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 840967, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 43324} | 1 |
construct-rlve-construct-hack-interval-l3-s9 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 3 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 7572720 (that is, 10 * 757272) such that
f(L) + f(L+1) + ... + f(R) is divisible by 757272.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The ... | {"mod": 757272, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 22, "R": 39140} | 1 |
construct-rlve-construct-hack-interval-l4-s0 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 2489598930 (that is, 10 * 248959893) such that
f(L) + f(L+1) + ... + f(R) is divisible by 248959893.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.js... | {"mod": 248959893, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 134398395, "R": 234398394} | 1 |
construct-rlve-construct-hack-interval-l4-s1 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 67499723810 (that is, 10 * 6749972381) such that
f(L) + f(L+1) + ... + f(R) is divisible by 6749972381.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 6749972381, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 6749806667, "R": 7749806666} | 1 |
construct-rlve-construct-hack-interval-l4-s2 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 62450929730 (that is, 10 * 6245092973) such that
f(L) + f(L+1) + ... + f(R) is divisible by 6245092973.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 6245092973, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3215650811, "R": 4215650810} | 1 |
construct-rlve-construct-hack-interval-l4-s3 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 76863023930 (that is, 10 * 7686302393) such that
f(L) + f(L+1) + ... + f(R) is divisible by 7686302393.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 7686302393, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 5617814358, "R": 6617814357} | 1 |
construct-rlve-construct-hack-interval-l4-s4 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 85226923390 (that is, 10 * 8522692339) such that
f(L) + f(L+1) + ... + f(R) is divisible by 8522692339.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 8522692339, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 2113461695, "R": 3113461694} | 1 |
construct-rlve-construct-hack-interval-l4-s5 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 99541285240 (that is, 10 * 9954128524) such that
f(L) + f(L+1) + ... + f(R) is divisible by 9954128524.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 9954128524, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 7889912104, "R": 17889912103} | 1 |
construct-rlve-construct-hack-interval-l4-s6 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 5275985880 (that is, 10 * 527598588) such that
f(L) + f(L+1) + ... + f(R) is divisible by 527598588.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.js... | {"mod": 527598588, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 93190116, "R": 193190115} | 1 |
construct-rlve-construct-hack-interval-l4-s7 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 61103773050 (that is, 10 * 6110377305) such that
f(L) + f(L+1) + ... + f(R) is divisible by 6110377305.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 6110377305, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 2272641135, "R": 3272641134} | 1 |
construct-rlve-construct-hack-interval-l4-s8 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 16717260200 (that is, 10 * 1671726020) such that
f(L) + f(L+1) + ... + f(R) is divisible by 1671726020.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 1671726020, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 1293150500, "R": 2293150499} | 1 |
construct-rlve-construct-hack-interval-l4-s9 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 4 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 50858646270 (that is, 10 * 5085864627) such that
f(L) + f(L+1) + ... + f(R) is divisible by 5085864627.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer... | {"mod": 5085864627, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 186917016, "R": 1186917015} | 1 |
construct-rlve-construct-hack-interval-l5-s0 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8464213534139900 (that is, 10 * 846421353413990) such that
f(L) + f(L+1) + ... + f(R) is divisible by 846421353413990.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 846421353413990, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 471370827311920, "R": 571370827311919} | 1 |
construct-rlve-construct-hack-interval-l5-s1 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 6743216346726580 (that is, 10 * 674321634672658) such that
f(L) + f(L+1) + ... + f(R) is divisible by 674321634672658.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 674321634672658, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 443216346726580, "R": 543216346726579} | 1 |
construct-rlve-construct-hack-interval-l5-s2 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 5577787032466150 (that is, 10 * 557778703246615) such that
f(L) + f(L+1) + ... + f(R) is divisible by 557778703246615.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 557778703246615, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 393344438959380, "R": 493344438959379} | 1 |
construct-rlve-construct-hack-interval-l5-s3 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8066857801535180 (that is, 10 * 806685780153518) such that
f(L) + f(L+1) + ... + f(R) is divisible by 806685780153518.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 806685780153518, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 153486241228144, "R": 253486241228143} | 1 |
construct-rlve-construct-hack-interval-l5-s4 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 4189678938585830 (that is, 10 * 418967893858583) such that
f(L) + f(L+1) + ... + f(R) is divisible by 418967893858583.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 418967893858583, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 403486301737328, "R": 503486301737327} | 1 |
construct-rlve-construct-hack-interval-l5-s5 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 2976261906436430 (that is, 10 * 297626190643643) such that
f(L) + f(L+1) + ... + f(R) is divisible by 297626190643643.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 297626190643643, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 10252381287286, "R": 20252381287285} | 1 |
construct-rlve-construct-hack-interval-l5-s6 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 2942080325364240 (that is, 10 * 294208032536424) such that
f(L) + f(L+1) + ... + f(R) is divisible by 294208032536424.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 294208032536424, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3416065072848, "R": 13416065072847} | 1 |
construct-rlve-construct-hack-interval-l5-s7 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 4459641404047750 (that is, 10 * 445964140404775) such that
f(L) + f(L+1) + ... + f(R) is divisible by 445964140404775.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 445964140404775, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 389462106071625, "R": 489462106071624} | 1 |
construct-rlve-construct-hack-interval-l5-s8 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 5447483341210300 (that is, 10 * 544748334121030) such that
f(L) + f(L+1) + ... + f(R) is divisible by 544748334121030.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 544748334121030, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 236980009452360, "R": 336980009452359} | 1 |
construct-rlve-construct-hack-interval-l5-s9 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 5 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 3719407932375660 (that is, 10 * 371940793237566) such that
f(L) + f(L+1) + ... + f(R) is divisible by 371940793237566.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `... | {"mod": 371940793237566, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 22993485038622, "R": 122993485038621} | 1 |
construct-rlve-construct-hack-interval-l6-s0 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8549225263483804140 (that is, 10 * 854922526348380414) such that
f(L) + f(L+1) + ... + f(R) is divisible by 854922526348380414.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 854922526348380414, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 44302737135423726, "R": 144302737135423725} | 1 |
construct-rlve-construct-hack-interval-l6-s1 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 2579411013043297330 (that is, 10 * 257941101304329733) such that
f(L) + f(L+1) + ... + f(R) is divisible by 257941101304329733.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 257941101304329733, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 53823303912989199, "R": 63823303912989198} | 1 |
construct-rlve-construct-hack-interval-l6-s2 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 1117620540829949760 (that is, 10 * 111762054082994976) such that
f(L) + f(L+1) + ... + f(R) is divisible by 111762054082994976.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 111762054082994976, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 62334378580964832, "R": 72334378580964831} | 1 |
construct-rlve-construct-hack-interval-l6-s3 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 4232790740303142110 (that is, 10 * 423279074030314211) such that
f(L) + f(L+1) + ... + f(R) is divisible by 423279074030314211.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 423279074030314211, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 392302406575970009, "R": 492302406575970008} | 1 |
construct-rlve-construct-hack-interval-l6-s4 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 4644409522383001810 (that is, 10 * 464440952238300181) such that
f(L) + f(L+1) + ... + f(R) is divisible by 464440952238300181.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 464440952238300181, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 245496188051103077, "R": 345496188051103076} | 1 |
construct-rlve-construct-hack-interval-l6-s5 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 7391257104415756650 (that is, 10 * 739125710441575665) such that
f(L) + f(L+1) + ... + f(R) is divisible by 739125710441575665.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 739125710441575665, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 19125710441575665, "R": 29125710441575664} | 1 |
construct-rlve-construct-hack-interval-l6-s6 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 8595336810246330060 (that is, 10 * 859533681024633006) such that
f(L) + f(L+1) + ... + f(R) is divisible by 859533681024633006.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 859533681024633006, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 85803129221697054, "R": 185803129221697053} | 1 |
construct-rlve-construct-hack-interval-l6-s7 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 6139929287327411310 (that is, 10 * 613992928732741131) such that
f(L) + f(L+1) + ... + f(R) is divisible by 613992928732741131.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 613992928732741131, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 331908073525634703, "R": 431908073525634702} | 1 |
construct-rlve-construct-hack-interval-l6-s8 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 6739855071340500590 (that is, 10 * 673985507134050059) such that
f(L) + f(L+1) + ... + f(R) is divisible by 673985507134050059.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 673985507134050059, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 437826085608600708, "R": 537826085608600707} | 1 |
construct-rlve-construct-hack-interval-l6-s9 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 6 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 9892538922998078260 (that is, 10 * 989253892299807826) such that
f(L) + f(L+1) + ... + f(R) is divisible by 989253892299807826.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as ... | {"mod": 989253892299807826, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 264031138398462608, "R": 364031138398462607} | 1 |
construct-rlve-crt-l1-s0 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 3 (mod 6)
x ≡ 0 (mod 5)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"moduli": [6, 5], "residues": [3, 0], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 15} | 1 |
construct-rlve-crt-l1-s1 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2 (mod 5)
x ≡ 0 (mod 7)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"moduli": [5, 7], "residues": [2, 0], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 7} | 1 |
construct-rlve-crt-l1-s2 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2 (mod 8)
x ≡ 0 (mod 2)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"moduli": [8, 2], "residues": [2, 0], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 10} | 1 |
construct-rlve-crt-l1-s3 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 4 (mod 15)
x ≡ 5 (mod 14)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"moduli": [15, 14], "residues": [4, 5], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 19} | 1 |
construct-rlve-crt-l1-s4 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 1 (mod 4)
x ≡ 7 (mod 10)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir... | {"moduli": [4, 10], "residues": [1, 7], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 17} | 1 |
construct-rlve-crt-l1-s5 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2 (mod 4)
x ≡ 3 (mod 7)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"moduli": [4, 7], "residues": [2, 3], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 10} | 1 |
construct-rlve-crt-l1-s6 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2 (mod 4)
x ≡ 0 (mod 6)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"moduli": [4, 6], "residues": [2, 0], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 6} | 1 |
construct-rlve-crt-l1-s7 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2 (mod 4)
x ≡ 2 (mod 3)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/... | {"moduli": [4, 3], "residues": [2, 2], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 14} | 1 |
construct-rlve-crt-l1-s8 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2 (mod 14)
x ≡ 3 (mod 13)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"moduli": [14, 13], "residues": [2, 3], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 16} | 1 |
construct-rlve-crt-l1-s9 | construct | rlve_crt | generalized_crt | number_theory | competition | 1 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 2 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 3 (mod 10)
x ≡ 0 (mod 13)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"moduli": [10, 13], "residues": [3, 0], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 13} | 1 |
construct-rlve-crt-l2-s0 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 15 (mod 30)
x ≡ 16 (mod 29)
x ≡ 9 (mod 18)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is... | {"moduli": [30, 29, 18], "residues": [15, 16, 9], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 45} | 1 |
construct-rlve-crt-l2-s1 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 25 (mod 145)
x ≡ 17 (mod 51)
x ≡ 2 (mod 6)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is... | {"moduli": [145, 51, 6], "residues": [25, 17, 2], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 170} | 1 |
construct-rlve-crt-l2-s2 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 8 (mod 10)
x ≡ 10 (mod 14)
x ≡ 17 (mod 21)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is... | {"moduli": [10, 14, 21], "residues": [8, 10, 17], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 38} | 1 |
construct-rlve-crt-l2-s3 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 73 (mod 76)
x ≡ 5 (mod 72)
x ≡ 17 (mod 132)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data i... | {"moduli": [76, 72, 132], "residues": [73, 5, 17], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 149} | 1 |
construct-rlve-crt-l2-s4 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 15 (mod 16)
x ≡ 25 (mod 51)
x ≡ 49 (mod 78)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data i... | {"moduli": [16, 51, 78], "residues": [15, 25, 49], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 127} | 1 |
construct-rlve-crt-l2-s5 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 35 (mod 40)
x ≡ 30 (mod 45)
x ≡ 3 (mod 9)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is ... | {"moduli": [40, 45, 9], "residues": [35, 30, 3], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 75} | 1 |
construct-rlve-crt-l2-s6 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 37 (mod 58)
x ≡ 66 (mod 87)
x ≡ 23 (mod 130)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data ... | {"moduli": [58, 87, 130], "residues": [37, 66, 23], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 153} | 1 |
construct-rlve-crt-l2-s7 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 30 (mod 34)
x ≡ 6 (mod 32)
x ≡ 4 (mod 6)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is a... | {"moduli": [34, 32, 6], "residues": [30, 6, 4], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 166} | 1 |
construct-rlve-crt-l2-s8 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 26 (mod 28)
x ≡ 6 (mod 19)
x ≡ 13 (mod 23)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is... | {"moduli": [28, 19, 23], "residues": [26, 6, 13], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 82} | 1 |
construct-rlve-crt-l2-s9 | construct | rlve_crt | generalized_crt | number_theory | competition | 2 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 3 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 13 (mod 24)
x ≡ 1 (mod 3)
x ≡ 1 (mod 4)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is al... | {"moduli": [24, 3, 4], "residues": [13, 1, 1], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 37} | 1 |
construct-rlve-crt-l3-s0 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 8 (mod 755)
x ≡ 2045 (mod 2493)
x ≡ 2 (mod 378)
x ≡ 1324 (mod 1607)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.js... | {"moduli": [755, 2493, 378, 1607], "residues": [8, 2045, 2, 1324], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 4538} | 1 |
construct-rlve-crt-l3-s1 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 476 (mod 4475)
x ≡ 1470 (mod 3481)
x ≡ 2363 (mod 2588)
x ≡ 901 (mod 1350)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/ans... | {"moduli": [4475, 3481, 2588, 1350], "residues": [476, 1470, 2363, 901], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 4951} | 1 |
construct-rlve-crt-l3-s2 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 912 (mod 3208)
x ≡ 1286 (mod 2834)
x ≡ 1070 (mod 3050)
x ≡ 982 (mod 1569)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/ans... | {"moduli": [3208, 2834, 3050, 1569], "residues": [912, 1286, 1070, 982], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 4120} | 1 |
construct-rlve-crt-l3-s3 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 219 (mod 316)
x ≡ 1179 (mod 1252)
x ≡ 326 (mod 421)
x ≡ 977 (mod 1454)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer... | {"moduli": [316, 1252, 421, 1454], "residues": [219, 1179, 326, 977], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 2431} | 1 |
construct-rlve-crt-l3-s4 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 126 (mod 165)
x ≡ 571 (mod 1205)
x ≡ 722 (mod 1054)
x ≡ 68 (mod 427)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.j... | {"moduli": [165, 1205, 1054, 427], "residues": [126, 571, 722, 68], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 1776} | 1 |
construct-rlve-crt-l3-s5 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 33 (mod 174)
x ≡ 15 (mod 16)
x ≡ 55 (mod 152)
x ≡ 22 (mod 37)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. T... | {"moduli": [174, 16, 152, 37], "residues": [33, 15, 55, 22], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 207} | 1 |
construct-rlve-crt-l3-s6 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2109 (mod 2515)
x ≡ 2275 (mod 2349)
x ≡ 600 (mod 4024)
x ≡ 649 (mod 795)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answ... | {"moduli": [2515, 2349, 4024, 795], "residues": [2109, 2275, 600, 649], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 4624} | 1 |
construct-rlve-crt-l3-s7 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 901 (mod 1028)
x ≡ 637 (mod 646)
x ≡ 337 (mod 1592)
x ≡ 100 (mod 1829)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer... | {"moduli": [1028, 646, 1592, 1829], "residues": [901, 637, 337, 100], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 1929} | 1 |
construct-rlve-crt-l3-s8 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 382 (mod 2367)
x ≡ 401 (mod 2348)
x ≡ 704 (mod 2045)
x ≡ 54 (mod 77)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.j... | {"moduli": [2367, 2348, 2045, 77], "residues": [382, 401, 704, 54], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 2749} | 1 |
construct-rlve-crt-l3-s9 | construct | rlve_crt | generalized_crt | number_theory | competition | 3 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 4 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 34 (mod 40)
x ≡ 15 (mod 179)
x ≡ 63 (mod 131)
x ≡ 74 (mod 120)
Answer format: {"x": <non-negative integer>}
Write your final answer as JSON to `/workdir/answer.json`. ... | {"moduli": [40, 179, 131, 120], "residues": [34, 15, 63, 74], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 194} | 1 |
construct-rlve-crt-l4-s0 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 1470 (mod 8702)
x ≡ 63529 (mod 103279)
x ≡ 8664 (mod 22592)
x ≡ 23396 (mod 23902)
x ≡ 10540 (mod 39067)
Answer format: {"x": <non-negative integer>}
Write your final a... | {"moduli": [8702, 103279, 22592, 23902, 39067], "residues": [1470, 63529, 8664, 23396, 10540], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 166808} | 1 |
construct-rlve-crt-l4-s1 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 20564 (mod 649311)
x ≡ 236497 (mod 433378)
x ≡ 200630 (mod 469245)
x ≡ 148789 (mod 260543)
x ≡ 59660 (mod 203405)
Answer format: {"x": <non-negative integer>}
Write yo... | {"moduli": [649311, 433378, 469245, 260543, 203405], "residues": [20564, 236497, 200630, 148789, 59660], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 669875} | 1 |
construct-rlve-crt-l4-s2 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 209947 (mod 434467)
x ≡ 59929 (mod 584485)
x ≡ 84534 (mod 139970)
x ≡ 273359 (mod 371055)
x ≡ 43994 (mod 60042)
Answer format: {"x": <non-negative integer>}
Write your... | {"moduli": [434467, 584485, 139970, 371055, 60042], "residues": [209947, 59929, 84534, 273359, 43994], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 644414} | 1 |
construct-rlve-crt-l4-s3 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 262300 (mod 268045)
x ≡ 425 (mod 44160)
x ≡ 197063 (mod 333282)
x ≡ 48304 (mod 482041)
x ≡ 20915 (mod 84905)
Answer format: {"x": <non-negative integer>}
Write your fi... | {"moduli": [268045, 44160, 333282, 482041, 84905], "residues": [262300, 425, 197063, 48304, 20915], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 530345} | 1 |
construct-rlve-crt-l4-s4 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 67085 (mod 95428)
x ≡ 145477 (mod 199374)
x ≡ 42565 (mod 83610)
x ≡ 43855 (mod 50037)
x ≡ 62611 (mod 80269)
Answer format: {"x": <non-negative integer>}
Write your fin... | {"moduli": [95428, 199374, 83610, 50037, 80269], "residues": [67085, 145477, 42565, 43855, 62611], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 544225} | 1 |
construct-rlve-crt-l4-s5 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 38003 (mod 93959)
x ≡ 61646 (mod 70316)
x ≡ 53416 (mod 78546)
x ≡ 4018 (mod 7108)
x ≡ 59102 (mod 72860)
Answer format: {"x": <non-negative integer>}
Write your final a... | {"moduli": [93959, 70316, 78546, 7108, 72860], "residues": [38003, 61646, 53416, 4018, 59102], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 131962} | 1 |
construct-rlve-crt-l4-s6 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 225 (mod 1935)
x ≡ 57620 (mod 886885)
x ≡ 184167 (mod 760338)
x ≡ 179799 (mod 764706)
x ≡ 42559 (mod 450973)
Answer format: {"x": <non-negative integer>}
Write your fi... | {"moduli": [1935, 886885, 760338, 764706, 450973], "residues": [225, 57620, 184167, 179799, 42559], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 944505} | 1 |
construct-rlve-crt-l4-s7 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 66026 (mod 121952)
x ≡ 73366 (mod 240234)
x ≡ 38576 (mod 257629)
x ≡ 27500 (mod 526334)
x ≡ 207365 (mod 346469)
Answer format: {"x": <non-negative integer>}
Write your... | {"moduli": [121952, 240234, 257629, 526334, 346469], "residues": [66026, 73366, 38576, 27500, 207365], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 553834} | 1 |
construct-rlve-crt-l4-s8 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 296524 (mod 684840)
x ≡ 485605 (mod 495759)
x ≡ 386354 (mod 595010)
x ≡ 471834 (mod 509530)
x ≡ 91974 (mod 177878)
Answer format: {"x": <non-negative integer>}
Write y... | {"moduli": [684840, 495759, 595010, 509530, 177878], "residues": [296524, 485605, 386354, 471834, 91974], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 981364} | 1 |
construct-rlve-crt-l4-s9 | construct | rlve_crt | generalized_crt | number_theory | competition | 4 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 5 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 5691 (mod 17945)
x ≡ 20956 (mod 55175)
x ≡ 12844 (mod 118462)
x ≡ 28920 (mod 51193)
x ≡ 11031 (mod 24055)
Answer format: {"x": <non-negative integer>}
Write your final... | {"moduli": [17945, 55175, 118462, 51193, 24055], "residues": [5691, 20956, 12844, 28920, 11031], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 131306} | 1 |
construct-rlve-crt-l5-s0 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 124385906 (mod 158298035)
x ≡ 366193326 (mod 1499470965)
x ≡ 917713262 (mod 947951029)
x ≡ 94890306 (mod 354154797)
x ≡ 466007585 (mod 699828353)
x ≡ 138251919 (mod 2879... | {"moduli": [158298035, 1499470965, 947951029, 354154797, 699828353, 287902062], "residues": [124385906, 366193326, 917713262, 94890306, 466007585, 138251919], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 1865664291} | 1 |
construct-rlve-crt-l5-s1 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 1015714744 (mod 1689557742)
x ≡ 274208535 (mod 5810179435)
x ≡ 2925635784 (mod 3158752186)
x ≡ 67495816 (mod 231418929)
x ≡ 518152197 (mod 795176539)
x ≡ 329203893 (mod ... | {"moduli": [1689557742, 5810179435, 3158752186, 231418929, 795176539, 5755184077], "residues": [1015714744, 274208535, 2925635784, 67495816, 518152197, 329203893], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 6084387970} | 1 |
construct-rlve-crt-l5-s2 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 53617477 (mod 3279395310)
x ≡ 3059600192 (mod 6832203215)
x ≡ 852156675 (mod 4519823366)
x ≡ 2045539018 (mod 2615421463)
x ≡ 554491437 (mod 933731197)
x ≡ 1257877261 (mo... | {"moduli": [3279395310, 6832203215, 4519823366, 2615421463, 933731197, 1438987691], "residues": [53617477, 3059600192, 852156675, 2045539018, 554491437, 1257877261], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 9891803407} | 1 |
construct-rlve-crt-l5-s3 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 25971426 (mod 699192753)
x ≡ 216672749 (mod 2351823974)
x ≡ 1790848934 (mod 3129471763)
x ≡ 868559058 (mod 1350587213)
x ≡ 666518614 (mod 4253802083)
x ≡ 1383927961 (mod... | {"moduli": [699192753, 2351823974, 3129471763, 1350587213, 4253802083, 1768196368], "residues": [25971426, 216672749, 1790848934, 868559058, 666518614, 1383927961], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 4920320697} | 1 |
construct-rlve-crt-l5-s4 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 7160562 (mod 147514872)
x ≡ 7402746 (mod 73636344)
x ≡ 17109108 (mod 22927721)
x ≡ 12168986 (mod 71253224)
x ≡ 2917704 (mod 10117182)
x ≡ 69369401 (mod 85306033)
Answer... | {"moduli": [147514872, 73636344, 22927721, 71253224, 10117182, 85306033], "residues": [7160562, 7402746, 17109108, 12168986, 2917704, 69369401], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 154675434} | 1 |
construct-rlve-crt-l5-s5 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2282541353 (mod 4582566970)
x ≡ 286296237 (mod 3289406043)
x ≡ 985674338 (mod 1175886797)
x ≡ 393755487 (mod 497796372)
x ≡ 1985950309 (mod 2439579007)
x ≡ 420227629 (mo... | {"moduli": [4582566970, 3289406043, 1175886797, 497796372, 2439579007, 920697242], "residues": [2282541353, 286296237, 985674338, 393755487, 1985950309, 420227629], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 6865108323} | 1 |
construct-rlve-crt-l5-s6 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 79160215 (mod 1327847258)
x ≡ 23488761 (mod 271136597)
x ≡ 975433210 (mod 1759421521)
x ≡ 369309777 (mod 1182772477)
x ≡ 70735085 (mod 1332059823)
x ≡ 841923135 (mod 946... | {"moduli": [1327847258, 271136597, 1759421521, 1182772477, 1332059823, 946465798], "residues": [79160215, 23488761, 975433210, 369309777, 70735085, 841923135], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 2734854731} | 1 |
construct-rlve-crt-l5-s7 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 2068962579 (mod 3138480415)
x ≡ 796168497 (mod 4411274497)
x ≡ 1701030237 (mod 3506412757)
x ≡ 2378177978 (mod 2829265016)
x ≡ 15070858 (mod 247255816)
x ≡ 2482831662 (m... | {"moduli": [3138480415, 4411274497, 3506412757, 2829265016, 247255816, 2724611332], "residues": [2068962579, 796168497, 1701030237, 2378177978, 15070858, 2482831662], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 5207442994} | 1 |
construct-rlve-crt-l5-s8 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 232122125 (mod 1560168774)
x ≡ 142292393 (mod 1605083640)
x ≡ 451836503 (mod 580124634)
x ≡ 1081095101 (mod 2271364572)
x ≡ 190662348 (mod 632359465)
x ≡ 718556341 (mod ... | {"moduli": [1560168774, 1605083640, 580124634, 2271364572, 632359465, 1316951666], "residues": [232122125, 142292393, 451836503, 1081095101, 190662348, 718556341], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 3352459673} | 1 |
construct-rlve-crt-l5-s9 | construct | rlve_crt | generalized_crt | number_theory | competition | 5 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 6 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 1406298 (mod 5861625)
x ≡ 269378613 (mod 1102539645)
x ≡ 107180465 (mod 3469817083)
x ≡ 1201156013 (mod 2375841535)
x ≡ 349253831 (mod 3227743717)
x ≡ 211950546 (mod 336... | {"moduli": [5861625, 1102539645, 3469817083, 2375841535, 3227743717, 3365047002], "residues": [1406298, 269378613, 107180465, 1201156013, 349253831, 211950546], "family": "rlve_crt", "subset": "construct"} | null | null | null | {"x": 3576997548} | 1 |
construct-rlve-crt-l6-s0 | construct | rlve_crt | generalized_crt | number_theory | competition | 6 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 15623008382971 (mod 16799074560376)
x ≡ 33146323976667 (mod 100070206328936)
x ≡ 12295310146698 (mod 24184244031781)
x ≡ 3420224519430 (mod 129796305786173)
x ≡ 17265682... | {"moduli": [16799074560376, 100070206328936, 24184244031781, 129796305786173, 38650282490168, 69001652881486, 13273824092374, 117741933522324], "residues": [15623008382971, 33146323976667, 12295310146698, 3420224519430, 17265682835099, 64214877424117, 478289381863, 15474596783279], "family": "rlve_crt", "subset": "cons... | null | null | null | {"x": 133216530305603} | 1 |
construct-rlve-crt-l6-s1 | construct | rlve_crt | generalized_crt | number_theory | competition | 6 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 215275172312746 (mod 627016053749209)
x ≡ 336280159741171 (mod 506011066320784)
x ≡ 388718354484776 (mod 453572871577179)
x ≡ 15387729361620 (mod 165380699340067)
x ≡ 66... | {"moduli": [627016053749209, 506011066320784, 453572871577179, 165380699340067, 110850560097054, 71869848300373, 19631030300707, 776488109295258], "residues": [215275172312746, 336280159741171, 388718354484776, 15387729361620, 66337305382577, 51722894757852, 17787953432261, 65803116766697], "family": "rlve_crt", "subse... | null | null | null | {"x": 842291226061955} | 1 |
construct-rlve-crt-l6-s2 | construct | rlve_crt | generalized_crt | number_theory | competition | 6 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 182711631042351 (mod 486808087331710)
x ≡ 38625243297313 (mod 210298158358916)
x ≡ 30989159003893 (mod 53210879947514)
x ≡ 1290852728501 (mod 83528608205695)
x ≡ 2527079... | {"moduli": [486808087331710, 210298158358916, 53210879947514, 83528608205695, 11910582829170, 628853003240228, 447710323222005, 361360120193456], "residues": [182711631042351, 38625243297313, 30989159003893, 1290852728501, 2527079940541, 40666715133833, 221809395152056, 308159598180605], "family": "rlve_crt", "subset":... | null | null | null | {"x": 669519718374061} | 1 |
construct-rlve-crt-l6-s3 | construct | rlve_crt | generalized_crt | number_theory | competition | 6 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 44403823089021 (mod 79172179552947)
x ≡ 25048082607657 (mod 256872279140205)
x ≡ 76955881404796 (mod 102482240171533)
x ≡ 45120266330207 (mod 47360019083531)
x ≡ 1291066... | {"moduli": [79172179552947, 256872279140205, 102482240171533, 47360019083531, 269009697272917, 23461103004080, 53361344325764, 103321432888646], "residues": [44403823089021, 25048082607657, 76955881404796, 45120266330207, 12910664474945, 387125698902, 15113640119042, 75277495970570], "family": "rlve_crt", "subset": "co... | null | null | null | {"x": 281920361747862} | 1 |
construct-rlve-crt-l6-s4 | construct | rlve_crt | generalized_crt | number_theory | competition | 6 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 81506636888873 (mod 436155846651882)
x ≡ 132858872705436 (mod 384803610835319)
x ≡ 45877985042183 (mod 117946124624643)
x ≡ 118682690109489 (mod 199489896715633)
x ≡ 660... | {"moduli": [436155846651882, 384803610835319, 117946124624643, 199489896715633, 255529932167324, 422153107918347, 503517654139142, 505613759245468], "residues": [81506636888873, 132858872705436, 45877985042183, 118682690109489, 6602619206107, 95509375622408, 14144829401613, 12048724295287], "family": "rlve_crt", "subse... | null | null | null | {"x": 517662483540755} | 1 |
construct-rlve-crt-l6-s5 | construct | rlve_crt | generalized_crt | number_theory | competition | 6 | RLVE-Gym/crt | MIT | [
"agentic_trivial"
] | Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
x ≡ 83837508535991 (mod 856749491349613)
x ≡ 2034656048496 (mod 21330735087207)
x ≡ 7042230731817 (mod 44454512816847)
x ≡ 82127064733868 (mod 107307491893967)
x ≡ 168208542... | {"moduli": [856749491349613, 21330735087207, 44454512816847, 107307491893967, 772378457491186, 528753489930346, 665853847519480, 196894342895235], "residues": [83837508535991, 2034656048496, 7042230731817, 82127064733868, 168208542394418, 411833509955258, 274733152366124, 153009628304664], "family": "rlve_crt", "subset... | null | null | null | {"x": 940586999885604} | 1 |
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