不定方程x^3+1=2019y^2的整数解

On the Integer Solution of the Indefinite Equation x^3+1=2019y^2

研究了不定方程x^3+1=2019y^2的整数解问题。利用简单同余法、分解因子法、Pell方程法以及分类讨论等初等方法,得出不定方程x^3+1=2019y^2有且仅有平凡整数解(x,y)=(-1,0)。

Using the simple congruence method,decomposition factor method,Pell equation method,classification discussion and other elementary methods to study the integer solution of the indefinite equation x^3+1=2019y^2 .It is proved that indefinite equation x^3+1=2019y^2 has only one integer solution(-1,0).