If a|b and b|a, find the value of a in terms of b.

Question

If a|b and b|a, where a and b are integers and a≠0, find the value of a in terms of b.

Assume that b>0.

Answer 1

Since $a|b \implies b=ak$ and $b|a \implies a=mb$.

Therefore that $$a=mb=mka \implies mk=1 \implies m=k=1 \text { or } m=k=-1 $$

So $a=\pm b$