Determine whether statement is true or false, and then prove answer.
For all integers $a,b,c$:
a) if $a|bc$ and gcd$(a,b) = 1$ then $a|c$
b) if $a|c$ and $a|b$ and gcd$(a,b) = 1$ then $ab|c$.
I've answered versions of these questions without the "and gcd$(a,b) = 1$", but I'm not sure if and how that affects whether the statement is true or false.
$\endgroup$ 41 Answer
$\begingroup$Bezout's identity. If $a$ and $b$ are relatively prime then there exist integers $x,y$ such that $ax+by=1$
Multiply both sides by $c$ for the first part and see what you can deduce.
$\endgroup$ 2
