Using binomial theorem, prove that `2^(3n)-7n-1` is divisible by `49` , where `n in Ndot`

Explanation

To prove that \(2^{3n} - 7n - 1\) is divisible by \(49\) using the binomial theorem, we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression \(2^{3n} - 7n - 1\). Notice that \(2^{3n}\) can be rewritten as \((2^3)^n = 8^n\). Thus, we can express our equation as:
\[ 8^n - 7n - 1 \]

...