关于Diophantine方程y^2-k=x^3的算术级数整数解

ON THE DIOPHANTINE y^2-k=x^3

讨论了由Monhanty提出的关于不定方程y^2-k=x^3的算术级数整数解,改进了一些结果,推翻了Monhanty提出的一些猜想.

Diophantine equation y2-k=x3 has a very long history. In 1975, S.P.Monhanty arised a new concept of solutions of this equation. It is one of integral solutions in arithmetic progression for y or x. We discussed this problem, improved some results, and negated S. P. Monhanty's some conjuctures.