关于不定方程组x^2-6y^2=1,y^2-Dz^2=4

Diophantine Equation x^2-6y^2=1,y^2-Dz^2=4

证明了当D=2k∏i=1pi,其中pi是互异的奇素数,且pi≡13,17,19,23(mod 24)时不定方程组x2-6y2=1,y2-Dz2=4仅有平凡解z=0.

It has been prored in this paper that when D=2kПi=1Pi ,where Pi should be odd primes, and Pi =13,17,19,23 （rood 24）,the simultaneous diophantine equations of x2 -6y2 = 1 and y2 - Dz2 =4 have the only integer solution z = 0.