- #1
mephillip
Homework Statement
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.
Homework Equations
pk=a
a=pq+r
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.