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Amazing number theory about polynomials

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 10.7

March 20, 2024
polynomialnumber theory

Problem Statement

Find all polynomials P(x)P(x) with integer coefficients, such that for any positive integer nn number P(n)P(n) is a positive integer and a divisor of n!n!.
Proposed by Mykyta Kharin
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