# Difference between revisions of "Pythagorean numbers"

From Encyclopedia of Mathematics

(Importing text file) |
(TeX) |
||

Line 1: | Line 1: | ||

− | Triplets of positive integers | + | {{TEX|done}} |

+ | Triplets of positive integers $x,y,z$ satisfying $x^2+y^2=z^2$. Any solution $x,y,z$ to this equation, and consequently all (possibly after switching $x$ only) Pythagorean numbers, can be expressed as $x=a^2-b^2$, $y=2ab$, $z=a^2+b^2$, where $a$ and $b$ are positive integers $(a>b)$. The Pythagorean numbers can be interpreted as the sides of a right-angled triangle (cf. [[Pythagoras theorem|Pythagoras theorem]]). | ||

## Revision as of 21:55, 11 April 2014

Triplets of positive integers $x,y,z$ satisfying $x^2+y^2=z^2$. Any solution $x,y,z$ to this equation, and consequently all (possibly after switching $x$ only) Pythagorean numbers, can be expressed as $x=a^2-b^2$, $y=2ab$, $z=a^2+b^2$, where $a$ and $b$ are positive integers $(a>b)$. The Pythagorean numbers can be interpreted as the sides of a right-angled triangle (cf. Pythagoras theorem).

#### Comments

#### References

[a1] | G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Chapt. XIII |

**How to Cite This Entry:**

Pythagorean numbers.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Pythagorean_numbers&oldid=11647

This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article