华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (1): 35-39,1.

• 数学 统计学 • 上一篇    下一篇

关于不定方程x3+1=38y2

段辉明   

  1. 重庆师范大学 数学与计算机学院, 重庆 400047
  • 收稿日期:2004-09-30 修回日期:2005-02-14 出版日期:2006-01-25 发布日期:2006-01-25
  • 通讯作者: 段辉明

On the Diophantine Equation x3+1=38y2(Chinese)

DUAN Hui-ming   

  1. Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
  • Received:2004-09-30 Revised:2005-02-14 Online:2006-01-25 Published:2006-01-25
  • Contact: DUAN Hui-ming

摘要： 利用递归数列和同余式证明了不定方程x3+1=38y2,仅有整数解(x,y)=(-1,0),(31,±28).

关键词: 不定方程, 整数解, 递归序列, 平方剩余, 不定方程, 整数解, 递归序列, 平方剩余

Abstract:

This paper has proved that the Diophantine equation x3+1=38y2 has only integer solutions(x,y)=(-1, 0),(31,±28).

Key words: Diophantine equation, recurrent sequence, quadratic remainder, integer solution, Diophantine equation, recurrent sequence, quadratic remainder

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