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Help fast on these 2 problems!  Find all positive integers n for which n^2 - 19n + 99 is a perfect square. I have tried and found 4 solutions 1,9,10,18 using a^2=n^2-19n+99 and then doing the discriminant. Where am I going wrong?

 

Second question: 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. I don't know how to start.

 Jul 15, 2020
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For the first problem, as a hint, look for large solutions.

 Jul 16, 2020

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