1. The problem statement, all variables and given/known data Show that if p is an irreducible integer, then for any integer a, either gcd(p,a)=1 or p divides a. 2. Relevant equations p is irreducible when p=ab and p is not equal to 0,1, or -1. And either a or b is invertible 3. The attempt at a solution Since p=ab, then p divides a. Suppose p does not divide a. Then gcd(p,a)=1. So there exists x and y such that px+ay=1. This is where I'm stuck. I don't know how to show that when p doesn't divide a, that the gcd(p,a)=1. Help please.