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Let p(x) be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive integers n such that p(n) is composite.

 Oct 22, 2021
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Let P(x) = x^2.  Then P(1) = 1, p(2) = 4, p(3) = 9, so p(n) is always a perfect square.  You can do this for any polynomial that factors, like P(x) = x^3 and P(x) = x(x + 1).

 Jan 5, 2022

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