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## Homework Statement

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 a

^{k}is congruent to b

^{k}(mod n).

## Homework 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.