benchmarks/Algorithms/euler_theorem_inverse/problem.md

Modular Inverse by Euler's Theorem

Description

For coprime positive integers value and modulus, compute the canonical multiplicative inverse of value modulo modulus using Euler's theorem.

Input

The function receives value and modulus.

Output

Return the unique integer $x$ in $[0,modulus)$ satisfying $value \cdot x \equiv 1 \pmod{modulus}$.

Constraints

• $0 < value < modulus$.
• $2 \le modulus \le 46341$.
• $\gcd(value,modulus)=1$.

Source

Classical number-theory problem reconstructed from the verified C artifact.