Using principle of mathematical induction, prove that `7^(4^(n)) -1` is divisible by `2^(2n+3)` for any natural number n.

Explanation

To prove that \( 7^{4^n} - 1 \) is divisible by \( 2^{2n + 3} \) for any natural number \( n \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We start with the base case \( n = 1 \).

\[ 7^{4^1} - 1 = 7^4 - 1 \]
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