Solutions of Pythagorean Equation/Examples/4, 3

Examples of Solutions of Pythagorean Equation

Setting $m = 4$ and $n = 3$ we obtain the primitive Pythagorean triple:

$\tuple {7, 24, 25}$

$\ds m$

$=$

$\ds 4$

by hypothesis

$\ds n$

$=$

$\ds 3$

by hypothesis

$\ds \leadsto \ \ $

$\ds 2 m n$

$=$

$\ds 2 \times 4 \times 3$

$\ds = 24$

$\ds m^2 - n^2$

$=$

$\ds 4^2 - 3^2$

$\ds = 7$

$\ds m^2 + n^2$

$=$

$\ds 4^2 + 3^2$

$\ds = 25$

$\blacksquare$

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pythagorean triple