For my homework one of the problems is the
Proposition: For all integers a and n, if a divides n^2 and a<=n then a divides n.
It either has to be proved or a counterexample given and I can't find a counterexample so I'm trying to prove it. I know that n^2 has to be positive but that isn't the case for a and n. n^2 would be equal to a times some integer so n^2 = a*x so n would be the square root of that. But in order to prove its divisible you have to prove that it is a times some integer and I cant prove the square root of a*x is an integer so I guess I just need some help with what I should do next. I haven't been doing proofs for long. Thanks for any help.