Let a and b be relatively prime integers. Prove the following facts: 1.Let c ∈ Z≥1 be relatively prime to both a and b. Then c and ab are also relatively prime. 2.For any integer n, we have that both...

Let a and b be relatively prime integers. Prove the following facts:

1.Let c ∈ Z≥1 be relatively prime to both a and b. Then c and ab are also relatively prime.

2.For any integer n, we have that both a | n and b | n if and only if ab | n.

3.For every integer m, there exist integers x and y such that ax + by = m.