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

Example of Aurifeuillian Factorizations

 * $2^{4 n + 2} + 1 = \left({2^{2 n + 1} - 2^{n + 1} + 1}\right) \left({2^{2 n + 1} + 2^{n + 1} + 1}\right)$

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

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

Then: