Difference of two squares

The identity

r^{2} - s^{2} = (r - s) (r + s)

converts a square difference into a factorization.

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- Fermat factorization method Difference of two squares

Fermat factorization method

Fermat factorization tests successive

r \geq ⌈ N ⌉

until

r^{2} - N = s^{2}

, then returns

N = (r - s) (r + s)

.

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Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 4 / 1H / Solution

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The "Difference of Two Squares" is a mathematical concept and a specific algebraic identity that expresses the difference between the squares of two quantities. It is represented by the formula: \[ a^2 - b^2 = (a - b)(a + b) \] In this equation: - \(a\) and \(b\) are any numbers or algebraic expressions. - \(a^2\) is the square of \(a\).

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