\begin{definition}[Definition:Aurifeuillian Factorization]
An '''Aurifeuillian factorization''' is an operation to find the prime factors of integers of various forms based upon the identity:
:$a^2 + b^2 = \left({a + \sqrt {2a b} + b}\right) \left({a - \sqrt{2ab} + b}\right)$
\end{definition}