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.

Jonjon Jul 15, 2020