# Thread: Direct proof for the following

1. ## Direct proof for the following

Suppose a, b, d, x, and y are integers. Prove that if d|a and d|b then d|(ax+by).

Pf: Since d|a and d|b then there exists two integers m and n such that dm = a and dn = b.

2. Originally Posted by algebrapro18
Suppose a, b, d, x, and y are integers. Prove that if d|a and d|b then d|(ax+by).

Pf: Since d|a and d|b then there exists two integers m and n such that dm = a and dn = b.
d|a means there is an A so that a=dA. d|b means there is a B so that b=dB. Now ax+by = dAx + dBy = d(Ax+By) and so d|(ax+by).

3. Wow I can't believe I didn't see that...so easy. The reason I asked this is because my professor made it sound MUCH harder than this.