III. Greatest Common Divisors
Problem 5 (10 points)
Suppose that $a|n$, $b|n$, and $gcd(a, b) = 1$ where $a$, $b$, and $n \in \mathbb{Z}^+$.
Prove that $(a \cdot b)|n$.
Hint: Recall that $gcd(a,b) = 1$ iff, for
some $x, y \in \mathbb{Z}$: $a \cdot x + b \cdot y = 1$.