关于不定方程x～3-1=Dy～2

On the Diophantine Equation x～3-1=Dy～2

证明了如下结果:如果题设方程有非平凡整数解,D只有唯一的6k+1形素因子p,则D要么没有其他素因子,要么任何其他素因子q都满足(3p/q)=1或(p/q)=1.

To prove that if the Diophantine equation mentioned in the title has a nontrivial solution （x ,y）in integers and D has only one prime factor p of the form 6k＋1, then either the integer D has no other prime factors or any prime factor q of D satisfies （3p/q）=1 or （p/q）=1.