1. The problem statement, all variables and given/known data I have to prove the following claim. Claim: For any positive integers m and n, m and n both greater than 1, if n|m and a≡b(mod m), then a≡b(mod n). 2. Relevant equations n/a 3. The attempt at a solution so i first changed each equation (ex: a≡b(mod m)) to a=b+qm and a=b+qn I figured in these forms I could show that the equations are equal. so I eventually get (a-b)/q=m or =n respectively. So I believe this shows their equality, but i am completely unsure because it won't always work I don't think. I need to also show that n|m. So tired dividing the m=(a-b)/q by the n= equation and of course I just get 1... To be completely honest I am not quite sure how to prove this. I am not quite familiar with the mod function and I am incredibly weak with proofs. If anyone can give me insight into solving this problem I would great appreciative. also note that this should be able to be done with a direct proof. thanks!