1. The problem statement, all variables and given/known data The problem went "If c|a and c|b then c|gcd(a,b) where cεN and a,bεZ" 2. Relevant equations 3. The attempt at a solution My proof went like this " Let a=cr and b=cs where r,sεZ. We want to show c|gcd(a,b). Lets start with cd=ax+by where d,x,yεZ since the gcd(a,b) can be rewritten as a linear combination. Substituting a and b we get cd=(cr)ax+(cs)ay <=> cd=c(rax+say) where rax+sayεZ. Hence c|gcd(a,b). is this right?