I have this problem from my class:

Let P be a nonconstant polynomial, where all the coefficients are non-negative integers. Prove that there exist infinitely many positive integers n such that P(n) is composite.


The hint is that P(A)-P(B) is divisible by A-B. I've first tried including that n = a-b. Therefore, my equation is n | P(n+2)-P(2). I do not know how to go on from here. Can someone help me out?

 Apr 24, 2020

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 Jul 24, 2020

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