I'm trying to solve this problem. I should be able to do it using simple divisibility properties but I don't know how.
Let a and b be integers such that they are coprime. Prove that $\gcd(a^2b^3,a+b)=1$
For instance... I thought that the gcd divides both $a^2b^3$ and $a+b$ so it must divide a sum of them. I've tried going this way but it's not clear to me where it should lead me. Any hint will be welcomed. Thanks.