关于丢番图方程x^3+y^3=pDz^2

On the Diophantine Equation x^3+y^3=pDz^2

设p≡ 5(mod6 )是素数,D是无平方因子且不被p和 6k +1形素数整除的正整数,运用初等数论方法,获得了丢番图方程x3 +y3 =pDz2 在D=1,2,3,6时全部整数解的通解公式及其解的深刻性质,从而推进了广义Fermat猜想与Tijdeman猜想的研究进展.

Let p≡5(mod6) is a prime, D>0 be a square free Integer With no prime factor p≡1(mod6).In This paper, We give all solutions of the diophantine equations x^3+y 3=pDz 2,(x,y)=1 respectively.