Prove the following by contraposition counterexample or cont

Prove the following by contraposition, counterexample or contradiction: Let

If n divides (a+b) and n divides a, then n divides b.

Solution

We prove by contradiction

Let, n divide a+b, and n divide a but n does not divide b

a+b=kn for some integer k

a=rn for some integer r

a+b-a=b=kn-rn=(k-r)n

Hence, n|b

THis is a contraditction

Hence, n divides b