1. The problem statement, all variables and given/known data I need to prove the following but have no idea how to do so. Let a,b, k be integers with k positive. If a is congruent to b(mod n), then ak is congruent to bk (mod n). 2. Relevant equations The hint given is that I can assume the following proposition is true and that I am supposed to use it to show the statement holds for k=2,3... Proposition: If a is congruent to b(mod n) and c is congruent to d(mod n) then a+c is congruent to b+d(mod n) Thanks for your help, I am pretty lost on this so anything helps.