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.

Hint: Remember that if $a$ and $b$ are distinct integers, then $P(a) - P(b)$ is divisible by $a - b.$

Please explain

Guest May 22, 2020

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Guest Jul 24, 2020