Euler's Factorization Method
Works by expressing 
as a Quadratic Form in two different ways. Then
 | (1) |
 | (2) |
 | (3) |
be the Greatest Common Divisor of 
and 
so |  |  | (4) |
 | |  | (5) |
 | |  | (6) |
(where
denotes the Greatest Common Divisor of 
and 
), and | (7) |
, 
and | (8) |
 | (9) |
 | |
 | |
 | |
 | |
 | (10) |