The hint is to use F_{a+b}= F_{a}F_{b+1}+ F_{a-1}F_{b}.

What i keep trying:

a divides b => there is a q in Z such that aq = b.

so aq + a = b + a, and then i use the hint.

But i never get anywhere.

I want to use that if a divides b and a divides c then a divides mb + nc for m,n in Z, but i can't figure out how/ I tried to let c = a, but I got nowhere.