# Polynomial with positive integer coefficients

Prove that if $$P(x)$$ is a polynomial with integer coefficients such that $$P(n)$$ is a perfect square for every integer $$n$$, the degree of $$P(x)$$ must be even.

• Tried using Diophantine equation but couldnot proceed – shirish Apr 12 at 17:20
• If it has odd degree, then it takes negative values. – user647486 Apr 12 at 17:23
• instead of pulling apart a perfect-square polynomial, try to consider how it may have been built. – John Joy Apr 13 at 14:35

Hint What is the behavior of an odd polynomial $$P(x)$$ as $$x \to \pm \infty$$?