[1]马米米,吴建东.关于丢番图方程(65n)x+(72n)y=(97n)z[J].南京师范大学学报(自然科学版),2014,37(04):28.
 Ma Mimi,Wu Jiandong.On the Diophantine Equation(65n)x+(72n)y=(97n)z[J].Journal of Nanjing Normal University(Natural Science Edition),2014,37(04):28.
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第37卷
期数:
2014年04期
页码:
28
栏目:
数学
出版日期:
2014-12-31

文章信息/Info

Title:
On the Diophantine Equation(65n)x+(72n)y=(97n)z
作者:
马米米吴建东
南京师范大学数学科学学院,数学研究所,江苏 南京 210023
Author(s):
Ma MimiWu Jiandong
School of Mathematical Sciences and Institute of Mathematics,Nanjing Normal University,Nanjing 210023,China
关键词:
Jesmanowicz猜想丢番图方程
Keywords:
Jesmanowicz conjectureDiophantine equation
分类号:
O156.1,O156.7
文献标志码:
A
摘要:
本文证明了对任意的正整数n,丢番图方程(65n)x+(72n)y=(97n)z仅有正整数解(x,y,z)=(2,2,2).
Abstract:
In this paper,we show that for any positive integer n,the Diophantine equation(65n)x+(72n)y=(97n)z has no solution other than(x,y,z)=(2,2,2)in positive integers.

参考文献/References:

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[2]Jesmanowicz L.Several remarks on Pythagorean numbers[J].Wiadom Mat,1955,1:196-202.
[3]Miyazaki T.Generallizatioins of classical results on Jesmanowicz’ conjecture concerning Pythagorean triples[J].J Number Theory,2013,133:583-595.
[4]Deng M J,Cohen G L.On the conjecture of Jesmanowicz concerning Pythagorean triples[J].Bull Austral Math Soc,1998,57:515-524.
[5]Yang Z J,Tang M.On the diophantine equation(8n)x+(15n)y=(17n)z[J].Bull Austral Math Soc,2012,86:348-352.
[6]Sun C F,Cheng Z.A conjecture of Jesmanowicz’ concerning Pythangorean triples[J].Adv Math,2014,43:267-275.
[7]Le M H.A note on Jesmanowicz’conjecture concerning Pythangorean triples[J].Bull Austral Math Soc,1999,59:477-480.
[8]Deng M J.A note on the Diophantine equation(na)x+(nb)y=(nc)z[J].Bull Austral Math Soc,2014,89:316-321.

相似文献/References:

[1]薛晓果,孟倩倩,张 彬,等.丢番图方程ax+by=n的一个注记(英文)[J].南京师范大学学报(自然科学版),2015,38(04):32.
 Xue Xiaoguo,Meng Qianqian,Zhang Bin,et al.A Remark of Diophantine Equation ax+by=n[J].Journal of Nanjing Normal University(Natural Science Edition),2015,38(04):32.

备注/Memo

备注/Memo:
收稿日期:2013-12-10.
基金项目:国家自然科学基金(11371195)、江苏省高校自然科学研究项目(13KJD110005).
通讯联系人:吴建东,博士,讲师,研究方向:组合数论.E-mail:05348@njnu.edu.cn
更新日期/Last Update: 2014-12-31