MathDB
Nice -- Find all polynomials f such that f(n) divides n!^k

Source: Taiwan 2014 TST1, Problem 2

July 18, 2014
algebrapolynomialmodular arithmeticinductionfunctionstrong inductionnumber theory proposed

Problem Statement

For a fixed integer kk, determine all polynomials f(x)f(x) with integer coefficients such that f(n)f(n) divides (n!)k(n!)^k for every positive integer nn.
Back to ProblemsView on AoPS