关于丢番图方程(33n)^(x)+(544n)^(y)=(545n)^(z)  

The Diophantine Equation(33n)^(x)+(544n)^(y)=(545n)^(z)

作　　者：华程 HUA Cheng(School of Mathematics and Physics,Taizhou University,Taizhou 225300,China)

机构地区：[1]泰州学院数理学院,江苏泰州225300

出　　处：《数学的实践与认识》2021年第22期308-312,共5页Mathematics in Practice and Theory

基　　金：江苏省自然科学基金(BK20171318);泰州学院教育改革研究课题(2018JGB05)。

摘　　要：运用初等方法证明了:对于任意的正整数n,除去x=y=z外,丟番图方程(33n)^(x)+(544n)^(y)=(545n)^(z)无其它的正整数解,即当a=33,b=544,c=545时,Jesmanowicz猜想成立.By elementary method,it is proved that for any positive integern,the Diophantine equation(33n)^(x)+(544n)^(y)=(545n)^(z) has no solutions in positive integer other than x=y=z=2.That is Jesmanowicz conjecture is true when a=33,b=544,c=545.

关 键 词：丢番图方程 正整数解 JESMANOWICZ猜想 

分 类 号：O156.7[理学—数学]