Question

Let a, b nonzero integers
a) Prove that if a, b are relative prime, then, there doesn't exist a prime p such that p|a and p|b
b) Prove that there is no a prime p such that p|a and p|b, then a, b are relative prime
Please, help.

Answer 1

a) suppose there exists such a prime \(p\), then \(\gcd(a,b) = kp\neq 1\)

Answer 2

(This is contrapositive proof)

Answer 3

Yes, I got it. Since part a and b look alike, I confused.