I'm not sure if it goes here or the section beyond calculus, so I'm just putting it here because it doesn't involve any calculus. 1. The problem statement, all variables and given/known data Suppose that (a,b)=1 [Greatest Common Divisor=1] and (a,c)=1. Does (bc, a)=1? 2. Relevant equations (a,b)=d=au+bv, where u and v are integers and d is the greatest common divisor of a and b. 3. The attempt at a solution OK, so I'm taking both of the facts I already know, that (a,b)=1 and (a,c)=1 and turning them into a useful equation: 1=au+bv, and 1=am+cn where u,v,m, and n are all integers. I know that my end goal is to find a(q)+bc(r)=1 However, I can't seem to find a way to get there. The closest I've gotten is by setting the two equal: au+bv=am+cn, and them multiplying by bc to get: abcu-abcm=bc2n+b2cv Then I factor and move them to the same side to find: 0=a(bcm-bcu)+bc(cn+bv) Which is not what I need. Am I going about this the completely wrong way? I have a feeling I'm mistaking a basic part of the proof, as a similar problem is also giving me trouble.