关于指数丢番图方程(a^(n)-1)((a+s)^(n)-1)=x^(2)可解性的研究  

On the solvability of Diophantine equation(a^(n)-1)((a+s)^(n)-1)=x^(2)

作　　者：罗永亮 杨海[1] 李恒 Luo Yongliang;Yang Hai;Li Heng(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：《纯粹数学与应用数学》2022年第1期127-132,共6页Pure and Applied Mathematics

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,整除,Pell方程等性质,其它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,给出判定方程无正整数解的三个充分条件,一定程度上拓展了方程无正整数解的范围,也进一步推广了前人的研究结果.By using the properties of congruence,division and Pell equation,other known conclusions and the methods of elementary number theory,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 judging the equation which has no positive integer solution were given.Then the range of the equation that have no positive integer solution was expanded and the previous results was improved.

关 键 词：指数丢番图方程 整除性质 PELL方程 正整数解 

分 类 号：O156.7[理学—数学]