1. The problem statement, all variables and given/known data If (a,c) = 1 and (b,c) = 1, prove that (ab,c) = 1. Note that (x,y) refers to the greatest common divisor between x and y. 2. The attempt at a solution There is a theorem that says since (a,c) = 1, there exist integers u and v such that au + cv = 1. Likewise, there also exist integers p and q such that bp + cq = 1. How though, could that be tied to the proof's conclusion, that there exist integers m and n such that (ab)m + cn = 1? Thanks all!