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integer polynomial , k does not divide P(i), i=1,..., k

Source: 2006 Spanish Mathematical Olympiad P1

July 20, 2018
polynomialinteger rootInteger Polynomialalgebra

Problem Statement

Let P(x)P(x) be a polynomial with integer coefficients. Prove that if there is an integer kk such that none of the integers P(1),P(2),...,P(k)P(1),P(2), ..., P(k) is divisible by kk, then P(x)P(x) does not have integer roots.
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