Can anyone help me prove if n divides a and n divides b, then n divides (ax + by).
I'm not sure if writing in the form of : a = nx and b = ny are still allowed to be used as x and y exists in the definition of the conclusion. I was thinking of using other variables such as: a = nc, and b = nd but I got stuck instead.
If $n$ divides $a$ then $a=nc$. If $n$ divides $b$ then $b=nd$.
So $ax+by=ncx+ndy=n(cx+dy)$, so $n $ divides $ax+by$.