MathDB
v_p(n!) hits each residue class infinitely often

Source: Baltic Way 2020, Problem 17

November 14, 2020
number theorymodular arithmetic

Problem Statement

For a prime number pp and a positive integer nn, denote by f(p,n)f(p, n) the largest integer kk such that pk∣n!p^k \mid n!. Let pp be a given prime number and let mm and cc be given positive integers. Prove that there exist infinitely many positive integers nn such that f(p,n)≡c(modm)f(p, n) \equiv c \pmod m.
Back to ProblemsView on AoPS