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Generalization of 10.7

Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 11.8

March 20, 2024
number theorypolynomial

Problem Statement

Find all polynomials P(x)P(x) with integer coefficients, such that for each of them there exists a positive integer NN, such that for any positive integer n≥Nn\geq N, number P(n)P(n) is a positive integer and a divisor of n!n!.
Proposed by Mykyta Kharin
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