关于不定方程x^3-1=19y^2

On the Diophantine Equation x^3+1=19y^2

利用两种初等的方法,即对方程取某个正整数M>1为模来制造矛盾的同余法和递归序列法,证明了不定方程x3 -1=19y2 仅有整数解(x,y)=(1,0),从而进一步的证明了方程x2 -19y2 =-13无整数解;方程x2 -3r2 =-3仅有整数解(1.0).

In this paper,the author has proved, with two method of contradictor recurrent sequences and congruence when modules of some positive integer M>1, that the Diophantine equation x^3+1=19y^2 has only integer solution(x,y)=(1,0).In fact,we have obtained a more general result that the only intager solution of the diophantine equation x^2-3y^2=-3 is(-1,0),and the diophantine equntion x^2-19y^2=-3,isn't interger solution.