Category:Definitions/Aurifeuillian Factorizations

This category contains definitions related to Aurifeuillian Factorizations.
Related results can be found in Category:Aurifeuillian Factorizations.

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

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

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