Show that the integral part of
` (5 sqrt(5) + 11)^(2n +1)` is even where ` n in N ` .

Explanation

To show that the integral part of \( (5\sqrt{5} + 11)^{2n + 1} \) is even for \( n \in \mathbb{N} \), we can follow these steps:

### Step 1: Define the Expression
Let \( x = (5\sqrt{5} + 11)^{2n + 1} \).

### Step 2: Use the Conjugate
We can also consider the conjugate expression:
\[
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