KURSCHAK 2016 Problem 3

If $p,q\in\mathbb{R}[x]$ satisfy $p(p(x))=q(x)^2$ , does it follow that $p(x)=r(x)^2$ for some $r\in\mathbb{R}[x]$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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