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b224933 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | import OAI.NumberTheory.Catalan.Arithmetic.FixedCanonicalIntegerBase
import OAI.NumberTheory.Catalan.Polynomial.FixedCanonicalCoefficientTables
namespace OAI
section
noncomputable section
open scoped BigOperators
namespace InternalCatalan
theorem fixedIntegerBaseCanonical_mod_coefficients (r : Fin 49) (k : Fin 48) :
(fixedIntegerBaseCanonical r k : ZMod 101) =
2 * (∑ i ∈ Finset.range 65,
(fixedCanonicalPCoeff r i : ZMod 101) * (fixedClearedMoment i k : ZMod 101)) -
3 * (∑ i ∈ Finset.range 65,
(fixedCanonicalDCoeff r i : ZMod 101) * (fixedClearedZeta i k : ZMod 101)) := by
simp only [fixedIntegerBaseCanonical, fixedCanonicalPCoeff_eq, fixedCanonicalDCoeff_eq,
Int.cast_sub, Int.cast_mul, Int.cast_sum, Int.cast_ofNat]
end InternalCatalan
end
end
end OAI
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