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Irreducible Proof Help

  1. Oct 3, 2011 #1
    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.
  2. jcsd
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