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关于一类广义Ramanujan-Nagell方程的正整数解
张正萍¹, 赵开明²
1.重庆科技学院数理学院, 重庆 401331;2.重庆求精中学, 重庆 400015

摘要:

本文研究了一类广义Ramanujan-Nagell方程有正整数解的条件.利用二次域中的重要理论,给出了一个典型的Ramanujan-Nagell方程的所有正整数解,推广了文献[1]和[2]的结果.

关键词: 广义Ramanujan-Nagell方程正整数解二次域

DOI：

分类号:O156.7

基金项目:重庆市自然科学基金项目(cstc2013jcyjA10049);重庆科技学院本科教育教学改革研究项目(201249).

ON THE POSITIVE INTEGER SOLUTIONS OF A CLASS OF GENERALIZED RAMANUJAN-NAGELL EQUATION

ZHANG Zheng-ping¹, ZHAO Kai-ming²

1.School of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China;2.Chongqing Refinement School, Chongqing 400015, China

Abstract:

In this paper, we studied the necessary condition for existence of the positive integer solutions of a class of generalized Ramanujan-Nagell equation. On the base of it, we gave all the positive integer solutions of a typical Ramanujan-Nagell equations, and generalized some results of reference [1] and [2].

Key words: generalized Ramanujan-Nagell equation positive integer solution quadratic fields