1. The problem statement, all variables and given/known data For integers a,b, and c, if a and c are relatively prime and c|ab, then c|b. Knowing that: For any integers p and q, there are integers s and t such that gcd(p,q) = sp + tq. The hint I'm given is that I should form an equation from the fact that they are "relatively prime." The last caveat is that I cannot use fractions at all in my proof. 2. Relevant equations 3. The attempt at a solution So my hang up is definitely the equation for relatively prime. As I understand it for relatively prime: gcd(a,c)=1. Then, I suppose I could just use the given equation to say that 1= sa + tc. (I believe this Bézout's identity). Then I have the following claim: If 1= sa + tc and ab=cn then b=cp. Where n and p are just integers. Then I can say that sa=1-tc. Then multiplying the second condition by 's' I'd have sab=scn. Combining them b(1-tc)=scn. But I can't do fractions so I'm not sure what to make of this, or if I've even started the problem correctly. I find it unlikely that my relatively prime equation is correct, or is what they intended me to do. Thanks for the suggestions.