# Proof: If d|a and d|b, then d|(a-b)

If you’re cheating on your homework, and found this through a websearch, then know your teacher can also find this. Do your own proof.

This is exercise 3.2 of Elementary Number Theory (pdf) by W. Edwin Clark.

We know that $d|a$ and $d|b$ so we write $a = kd$ and $b = ld$.

Now $a-b = kd - ld$ which we can also write as $d(k - l)$. It is now obvious that $a-b = d(k - l)$, q.e.d.

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