Simon's Favorite Factoring Trick
Statement of the factorization
Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: .
This factorization was first popularized by AoPS user ComplexZeta, whose name is Simon.
This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually and are variables and are known constants. Also it is typically necessary to add the term to both sides to perform the factorization.
(AIME 1987/5) and are integers such that . Find .
Outline Solution: Rearrange to . The key step is changing the equation to , where the equation factors to , from which the problem is trivial to solve by applying some simple number theory.