Simon's Favorite Factoring Trick
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Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization first popularized by AoPS user Simon Rubinstein-Salzedo. <url>viewtopic.php?highlight=factoring&t=8215 This</url> appears to be the thread where Simon's favorite factoring trick was first introduced.
Statement of the factorization
The general statement of SFFT is: . Two special cases appear most commonly: and .
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.
Two different prime numbers between and are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?
- are integers such that . Find .
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