Use induction to prove that for every natural number n, 33n−1 is divisible by 26.
I can see that for n=1, 33−1=26⋅1. As for inductive step, assuming that the statement holds for n=k (33k−1=26k), I want to show it for n=k+1 (that is, 33(k+1)−1=26(k+1)). But how to proceed from here?
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