I have done it, but I am not sure that the inductive step is right. Can anybody please clear me about it?
Basic steps as:
Taking $n=1$: $p(1)=5-1=4$.
Inductive hypothesis: Assume the statement is true for $p(k)$. $5^k - 1$ is divisible by $4$.
Inductive steps: We must show $p(k+1)$ is true when $p(k)$ is true. \begin{align*} & 5^k -1 + 5^{k+1} -1\\ & 5^k -1 + 5.5^{k} -1\\ & (5^k -1) + 4 \end{align*}
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