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Proof of P(a^2)\neq 1

Source: 2008 Japan Mathematical Olympiad Finals Problem 1

February 12, 2008
algebrapolynomialnumber theoryrelatively primealgebra proposed

Problem Statement

Let P(x) P(x) be a polynomial with integer coefficients such that P(n^2) \equal{} 0 for some non zero integers n. n. Prove that P(a2)≠1 P(a^2)\neq 1 for all non zero rational numbers a≠0. a\neq 0.
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