MathDB
Control prime powers dividing product of polynomial values

Source: German TST 2023, Test 4, Problem 3

July 15, 2023
algebrapolynomialnumber theoryprime numbersalgebra proposed

Problem Statement

Let f(x)f(x) be a monic polynomial of degree 20232023 with positive integer coefficients. Show that for any sufficiently large integer NN and any prime number p>2023Np>2023N, the product f(1)f(2)…f(N)f(1)f(2)\dots f(N) is at most (20232)\binom{2023}{2} times divisible by pp. Proposed by Ashwin Sah
Back to ProblemsView on AoPS