关于丢番图方程(a^(n)+2^(m))(b^(n)+2^(m))=x^(2)  

On Diophantine Equation(a^(n)+2^(m))(b^(n)+2^(m))=x^(2)

作　　者：杨睿 罗家贵 YANG Rui;LUO Jiagui(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2021年第2期121-125,共5页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871058);四川省教育厅重大培育项目(16ZA0173)。

摘　　要：指数丢番图方程是一类重要的丢番图方程。国内外许多学者对丢番图方程(a^(n)-1)(b^(n)-1)=x^(2)进行了研究,并取得了一系列重要的结果。本文利用费马无穷递降法、Stormer定理及其推广、Lehmer序列的经典结论和Pell方程解的基本性质得到了丢番图方程(a^(n)+2^(m))(b^(n)+2^(m))=x^(2)无解的充分条件,从而推进序列有无平方项这类问题的研究。As an important class of Diophantine equations,exponential Diophantine equation has been studied by many scholars at home and abroad.A series of important results has been achieved in the study of Diophantine equation(a^(n)-1)(b^(n)-1)=x^(2).In this paper,the sufficient condition for Diophantine equation(a^(n)+2^(m))(b^(n)+2^(m))=x^(2) is obtained by the method of Fermat infinite descent,Stormer theorem and its extension,classic conclusions of Lehmer sequence and basic properties of Pell equation solution so as to advance the research on whether the sequence has a square term or not.

关 键 词：丢番图方程 PELL方程 Lehmer序列 基本解 最小解 

分 类 号：O156.7[理学—数学]