Solutions of Pythagorean Equation/Examples/6, 1

Examples of Solutions of Pythagorean Equation

Setting $m = 6$ and $n = 1$ we obtain the primitive Pythagorean triple:

$\tuple {12, 35, 37}$

$\ds m$

$=$

$\ds 6$

by hypothesis

$\ds n$

$=$

$\ds 1$

by hypothesis

$\ds \leadsto \ \ $

$\ds 2 m n$

$=$

$\ds 2 \times 6 \times 1$

$\ds = 12$

$\ds m^2 - n^2$

$=$

$\ds 6^2 - 1^2$

$\ds = 35$

$\ds m^2 + n^2$

$=$

$\ds 6^2 + 1^2$

$\ds = 27$

$\blacksquare$

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