1. The problem statement, all variables and given/known data 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 2. Relevant equations 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. Thm. If a and b are relatively prime then there exist integers m, n such that ma+nb=1. 3. The attempt at a solution It just seems so intuitive ... I don't know where to start.