I've tried to solve this problem, but I keep getting stuck at the end.
Assume $a, b$ , and d are integers and $d$ $\neq$ 0.
$3a+2b = dm,\,\,\,$ for some integer $m$.
$2a+b = dn,\,\,\,$ for some integer $n$.
$3a+2b - 2a - b = dm - dn$.
$a + b = d(m-n)$.
That's where I'm stuck now, because $a=d(m-n)-b or b=d(m-n)-a$ doesn't prove $d\mid a$ or $d\mid b$, unless I'm missing something or took a wrong turn somewhere.
Please help me, and thank you ahead of time.