Don't have the book with me, but the problem basically asked me to prove that
gcd(a,b)=1 [tex]\Rightarrow[/tex] gcd(an,bn)=n
Since gcd(a,b)=1 is a fancy way of saying a and b are relatively prime (or is "a and b are relatively prime" a fancy way of saying gcd(a,b)=1?), I know of a theorem that may prove useful.
If a and b are relatively prime then there exist integers m, n such that ma+nb=1.
The Attempt at a Solution
It just seems so intuitive ... I don't know where to start.