1. The problem statement, all variables and given/known data Let r,s,t and v be integers with r>0. If st=r+v and gcd(s,t)=r, then gcd(v,t)=r 2. Relevant equations Just stumped. I am not sure what to do next. 3. The attempt at a solution There are 2 integers d and e such that S=dR and T=eR, and 2 integers a and b such that Sa+Tb=R. I know I have to end with something like V(integer)+T(integer)=R to show the gcd(v,t)=r.