Definition:Aurifeuillian Factorization

Definition
An Aurifeuillian factorization is an operation to find the prime factors of integers of various forms based upon the identity:


 * $a^2 + b^2 = \paren {a - \sqrt {2 a b} + b} \paren {a + \sqrt {2 a b} + b}$


 * $a^3 + b^3 = \paren {a + b} \paren {a - \sqrt {3 a b} + b} \paren {a + \sqrt {3 a b} + b}$

Also known as
The term Aurifeuillian can also be seen as Aurifeuillean.