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Divisibility with a quadratic and a factorial

Source: Romania TST 2023 Day 2 P3

April 7, 2024
number theoryfactorialDivisibility

Problem Statement

Given a positive integer a,a, prove that n!n! is divisible by n2+n+an^2 + n + a for infinitely many positive integers n.n.{}
Proposed by Andrei Bâra
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