Show that the integral part of
` (5 + 2 sqrt(6))^(n) ` is odd where n is natural number

Explanation

To show that the integral part of \( (5 + 2\sqrt{6})^n \) is odd for any natural number \( n \), we can follow these steps:

### Step 1: Define the Expression
Let \( x = (5 + 2\sqrt{6})^n \). We will also consider its conjugate \( y = (5 - 2\sqrt{6})^n \).

### Step 2: Analyze the Conjugate
Notice that \( 5 - 2\sqrt{6} \) is a positive number less than 1 (since \( 2\sqrt{6} \approx 4.898 \), thus \( 5 - 2\sqrt{6} \approx 0.102 \)). Therefore, as \( n \) increases, \( y \) approaches 0.

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