1. The problem statement, all variables and given/known data Prove or disprove: let a and b be integers and let p be a prime number. If p divides ab then p divides a or p divides b. 2. Relevant equations pk=a a=pq+r 3. The attempt at a solution Contrapositive: if p does not divide a and p does not divide b, then p does not divide ab. p divides a for some integer k; pk=a p does not divide a for some integer q and r; a=pq+r If p divides ab and p does not divide a, then p divides b. gcd(p,a)=1; there exists integers u and v such that pu+av=1.