# Prove: If $d|a$ and $d|b$ then $d^2|ab$

Prove: If $d|a$ and $d|b$ then $d^2|ab$

All I have $ab = kd^2$, $k$ some integer. I'm stuck and hoping someone could walk me through this!

• We have $a=da'$ for some $a'$, same for $b$, so $ab=d^2(a'b')$. – André Nicolas Jul 17 '15 at 23:37

If $d|a$, then $a = dn$ for some integer $n$. If $d|b$, then $b = dm$ for some integer $m$. Multiply $a$ and $b$ together: $ab = (dn)(dm) = d^2mn$ which is exactly what $d^2|ab$ means.