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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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For the community: Please don't submit solutions to this problem. This is a homework problem for an online course that does not allow students to search for answers to specific problems outside of the school.

 

For the original poster: We realize that homework can be challenging. If you wish to receive help from the staff or other students, we encourage you to use the resources that the online classes provide. Please don't ask or search online for homework help. We understand that it's common in today's information age to look for resources online, and in some contexts, that's a great thing! However, it's against our Honor Code. You can ask for help on the message boards, and you can learn from the official solution after you submit your answer.

 Jul 24, 2020

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