不定方程x^2+64=y^(13)的整数解  

The Integer Solution on Diophantine Equation x^2+64 =y^(13)

作　　者：孙树东[1] 

机构地区：[1]新疆警察学院信息安全工程系,新疆乌鲁木齐830011

出　　处：《吉林师范大学学报（自然科学版）》2015年第3期78-80,共3页Journal of Jilin Normal University:Natural Science Edition

基　　金：新疆维吾尔自治区高校科研计划重点项目(XJEDU2008I31)

摘　　要：不定方程的整数解的研究是数论中一项重要的研究课题之一.在高斯环中,讨论了不定方程x2+64=y13的整数解问题,利用代数数论的方法证明了其无整数解的结论,推进了形如Ax2+B=yn这一类方程的研究.It is an important research topic to study the integer solution of Diophantine equation in number theory.In Gauss domain ,the integer solution on x2 ＋64=y13 was discussed ,and a conclusion that the diophantine equation x2 ＋64=y13 had no integer solution was given by using algebraic number theory in this paper ,which advanced the study of the form Ax2 ＋B=yn Diophantine equation.

关 键 词：不定方程 整数解 整环 

分 类 号：O156[理学—数学]