The greatest divisor of
`(a-b)(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)` is :

Options

A. `a^16-b^16`
B. `a^16+b^16`
C. `a^31-b^31`
D. `a^32-b^32`

Explanation

To find the greatest divisor of the expression \((a-b)(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^{16}+b^{16})\), we can simplify and analyze the terms step by step.

### Step 1: Rewrite the expression
We start with the given expression:
\[ (a-b)(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^{16}+b^{16}) \]

...