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Integer Coefficient Polynomial with order

Source: 2019 Korea Winter Program Practice Test 1 Problem 3

January 12, 2019
algebrapolynomialnumber theory

Problem Statement

Find all polynomials P(x)P(x) with integer coefficients such that for all positive number nn and prime pp satisfying p∤nP(n)p\nmid nP(n), we have ordp(n)≥ordp(P(n))ord_p(n)\ge ord_p(P(n)).
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