The base case is pretty straightforward. But I'm stuck on the inductive step.
As the base case holds, assume for when n=k holds, show the k+1 case holds true.
Inductive Hypothesis: a^k \equiv b^k \pmod m, then
a^{k+1} \equiv b^{k+1} \pmod m \iff a^{k+1} - b^{k+1} = m(k), k \in \mathbb{Z}.
I think I'm missing some steps, I'm not sure how to manipulate what I have to shows it holds.
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