不定方程组x^2-6y^2=1,y^2-Dz^2=4

The Integer Solution of the Simultaneous Diophantine Equations x^2-6y^2=1 and y^2-Dz^2=4

设D为奇数且最多含有3个互不相同的素因数,证明了不定方程组x2-6y2=1,y2-Dz2=4仅有两组非平凡解D=11,(x,y,z)=(49,20,6)和D=11×89×109,(x,y,z)=(4801,1960,6)。

The follwing conclusion is proved ： If D 〉 0 is an odd square - free integer which has at most three distinct prime factors, then the equation in title only have two non - trivial solutions D = 11, （x ,y,z） = （49,20,6） and D 11 ×89 × 109, （x,y,z） = （4801,1960,6）.