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May 13, 2007
algebrapolynomialinductioncalculusintegrationabstract algebrageometry

Problem Statement

Let P(x)∈Z[x]P(x)\in \mathbb{Z}[x] be a monic polynomial with even degree. Prove that, if for infinitely many integers xx, the number P(x)P(x) is a square of a positive integer, then there exists a polynomial Q(x)∈Z[x]Q(x)\in\mathbb{Z}[x] such that P(x)=Q(x)2P(x)=Q(x)^2.
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