Use induction to prove that for every natural number $n$, $ 3^{3n} - 1$ is divisible by $26$.
I can see that for $n=1$, $ 3^{3} -1=26\cdot 1$. As for inductive step, assuming that the statement holds for $n=k$ ($3^{3k}-1 = 26k$), I want to show it for $n=k+1$ (that is, $3^{ 3(k+1)} -1=26(k+1)$). But how to proceed from here?
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