A new proof of Legendre's theorem on the Diophantine equation $a{x}^2+b{y}^2+c{z}^2=0$

Jingbo Liu, Bruce McOsker

One of Legendre's theorems on the Diophantine equation $a{x}^2+b{y}^2+c{z}^2=0$ provides necessary and sufficient conditions on the existence of nonzero rational solutions of this equati…