1. The problem statement, all variables and given/known data Let a and b be relatively prime. Show that gcd(a+b,ab) = 1 2. Relevant equations ax+by = 1 for some integers x and y 3. The attempt at a solution I set gcd(a+b,ab) = d. I'm now trying to show that d = 1 using elementary algebra techniques. a+b = rd ab = sd ax + by = 1 I'm kind of stuck here.. am I on the right track? Do I just need to aggresively rearrange stuff until I can express (a+b) and (ab) as a linear combination that equals one? or perhaps arrange them in such away that I show d divides both a and b individually and therefore it must be one since they are relatively prime? any hints? Update: a+b = rd ---> b = rd -a ab = a(rd-a) = (ard)-(a^2) = sd dividing both sides by d... ar - (a^2 / d) = s ar is an integer and s is an integer, so a^2 / d must be an integer, therefore d|a^2. I employed a similar argument to show that d|b^2. Since d|a^2 and d|b^2 and gcd(a,b) = 1, we can use the fact that gcd(a^2,b^2) = 1 to conclude that d = 1. Is this a solid argument?