关于丢番图方程x^(2)+144=my^(11)(m=1,2,3,4,6)的整数解  

The Integer Solution on Diophantine Equation x^(2)+144=my^(11)(m=1,2,3,4,6)

作　　者：陈一维 白建慧 CHEN Yiwei;BAI Jianhui(College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《河南教育学院学报（自然科学版）》2021年第2期9-15,共7页Journal of Henan Institute of Education(Natural Science Edition)

摘　　要：在高斯整环中,利用代数数论与同余理论的方法,讨论了丢番图方程x^(2)+144=my^(11)(m=1,2,3,4,6)的整数解问题,并证明了丢番图方程x^(2)+144=my^(11)(m=1,2,3,4,6)无整数解。In Gauss domain,the problem of integer solution of the Diophantine equation x^(2)+144=my^(11)(m=1,2,3,4,6)is discussed by using the methods of algebraic number theory and congruence theory.It is proved that the Diophantine equation x^(2)+144=my^(11)(m=1,2,3,4,6)has no integer solution.

关 键 词：高斯整环 代数数论 同余理论 丢番图方程 整数解 

分 类 号：O156.4[理学—数学]