MathDB
Polynomial equiv factorial modulo prime

Source: KoMaL A815

March 19, 2022
number theory

Problem Statement

Let qq be a monic polynomial with integer coefficients. Prove that there exists a constant CC depending only on polynomial qq such that for an arbitrary prime number pp and an arbitrary positive integer N≤pN \leq p the congruence n!≡q(n)(modp)n! \equiv q(n) \pmod p has at most CN23CN^\frac {2}{3} solutions among any NN consecutive integers.
Back to ProblemsView on AoPS