关于丢番图方程x^3±5~6=Dy^2

On the Diophantine Equation x^3 ±5~6 =Dy^2

研究丢番图方程x3±56=Dy2,给出了当D>0,D无平方因子,且不能被3或6k+1型素数整除时的全部非平凡解。

Thispaper is a study of the Diophantine equation x 3 ±5 6 =Dy 2 .Provided D>0and d D,d≠3,d is not prime of the form6k+1,then equation x 3 +5 6 =Dy 2 have Six nontrivial integer solution:(1,0,125),(1,50,375 ),(2,25,125),(2,575,9750),(10,-15,35),(5 06,481,496)and the equation x 3 -5 6 =Dy 2 have only two nontrivial integer Solu-tion:(55,80,95)and(43 1,456,469).