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).
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...
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.