关于丢番图方程x^3±y^6=Dz^2(Ⅱ)

On the Diophantine Equation x^3±y^6=Dz^2(Ⅱ)

设D是无平方因子且不被 6k+1形素数整除的正整数 ,证明了丢番图方程x3±y6 =3z2 ,x3+y6 =6z2x3-y6 =z2 ,x3-y6 =2z2 均无yz≠ 0的整数解 ,方程x3+y6 =z2 仅有整数解 1+2 3=32 ,方程x3+y6 =2z2 和x3-y6 =6z2 均有无穷多组正整数解 ,并且获得了全部正整数解的通解公式 。

Let D >0 be a square free integer with no prime factor in this paper we give all solutions of the diophantine equations x 3±y 6=Dz 2 respectively.