关于指数丢番图方程((mk_(1)+m_(1))^(n)-1)((mk_(2)+m_(2))^(n)-1)=x^(2)的求解  

On the solution of exponential Diophantine equation((mk_(1)+m_(1))^(n)-1)((mk_(2)+m_(2))^(n)-1)=x^(2)

作　　者：罗永亮 杨海[1] 陈江涛 LUO Yong-liang;YANG Hai;CHEN Jiang-tao(School of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《西南民族大学学报（自然科学版）》2023年第4期457-462,共6页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11226038,11371012);陕西省自然科学基金(2021JM443)。

摘　　要：运用同余、二次剩余、勒让德符号、雅可比符号的性质、其他已知结论以及初等数论方法,研究了一类与平方数有关的指数丢番图方程的可解性问题.通过将方程的参数限定在一定的数量关系下,给出了方程在特定条件下不存在正整数解的三个充分条件,进一步推广了前人的研究成果,同时可为解决此类与平方数有关的指数丢番图方程提供了一定思路和方法.By using the properties of congruence,Quadratic residue,Legendre symbol,Jacobi symbol,other known conclusions and elementary number theory methods,the solvability of a class of exponential Diophantine equation involving square number was studied.If the parameters of equation were limited in a certain quantitative relationship,three sufficient conditions for the equation with no positive integer solution under certain condition were given,which further generalized the previous research results.At the same time,it provided some ideas and methods for solving such exponential Diophantine equation related to square number.

关 键 词：指数丢番图方程 勒让德符号 雅可比符号 同余 正整数解 

分 类 号：O156.7[理学—数学]