Aurifeuillian Factorization/Examples/2^4n+2 + 1

Example of Aurifeuillian Factorization

 * $2^{4 n + 2} + 1 = \paren {2^{2 n + 1} - 2^{n + 1} + 1} \paren {2^{2 n + 1} + 2^{n + 1} + 1}$

Proof
From Sum of Squares as Product of Factors with Square Roots:
 * $x^2 + y^2 = \paren {x + \sqrt {2 x y} + y} \paren {x - \sqrt {2 x y} + y}$

Let $x = 2^{2 n + 1}$ and $y = 1$.

Then: