Legendre's equation
id:
legendre-s-equation-185-2376256
title:
Legendre's equation
text:
In mathematics, Legendre's equation is the Diophantine equation a x 2 + b y 2 + c z 2 = 0. The equation is named for Adrien-Marie Legendre who proved in 1785 that it is solvable in integers x, y, z, not all zero, if and only if
−bc, −ca and −ab are quadratic residues modulo a, b and c, respectively, where a, b, c are nonzero, square-free, pairwise relatively prime integers, not all positive or all negative.
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Legendre%27s_equation
date created:
2006-04-18T03:59:49Z
date modified:
2024-09-07T15:09:23Z
main entity:
{"identifier":"Q4454970","url":"https://www.wikidata.org/entity/Q4454970"}
image:
fields total:
13
integrity:
14