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integer polynomial with P(x_1) = P(x_2) = ... = P(x_m) = 1, no integer roots

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1986 p2

February 17, 2020
algebrapolynomialInteger PolynomialInteger

Problem Statement

Let P(x)P(x) be a polynomial with integer coefficients of degree n≥3n \ge 3. If x1,...,xmx_1,...,x_m (n≥m≥3n\ge m\ge3) are different integers such that P(x1)=P(x2)=...=P(xm)=1P(x_1) = P(x_2) = ... = P(x_m) = 1, prove that PP cannot have integer roots$.
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