# Polynomial whose only values are squares

Given a polynomial $P \in \Bbb Z [X]$ such that, $P (x)$ is the square of an integer for all integers x, is $P$ necessarily of the form $P (x)= Q (x)^2$ with $Q \in \Bbb Z [X]$?

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## 1 Answer

Yes, see this answer, which gives a proof, and references this article, which deals with the multivariate case.

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