关于Diophantine方程x^2-s(s+1)y^2=1与y^2-2~nz^2=4的公解

摘要

本文证明了当s,n∈Z^+时Diophantine方程x^2-s(s+1)y^2=1与y^2-2~nz^2=4除开s=2且n=1,3,5外仅有平凡解(x,y,z)=(±5,±2,0).