I've been working on these two problems for the last few days, can't seem to get it. Any help would be very much appreciated.

1. Prove that a|bc iff a/(a,b)|c

So far I know that the denominator has to be a common multiple of both a & b, but I cannot prove that it has to be the gcd of a & b.

2. Show that if (a,b)=1, then (a+b,a2-ab+b2)=1 or 3

So far this is what I've come up with, using the theorems:

a) (a,m)=1, (b,m)=1, then (ab,m)=1

b) (a,b)=(a,b+na) that:

(a(a+b),b) = (a2+ab,b) = 1

(a,b(b-2a)) = (a,b2-2ab)=1

but I can't seem to relate the two.

Again, thanks for any help in advance.