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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 $n$ $P(n)$ such that  is composite.

 May 7, 2022
 #1
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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.

 May 7, 2022
 #2
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This is obvious if you use the following fact: If m and n are integers, then m - n divides P(m) - P(n).

 May 7, 2022

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