凌灯荣,翁建欣

(安徽师范大学数学计算机科学学院,安徽芜湖 241003)

关于丢番图方程(195n)x+(28n)y=(197n)z

凌灯荣,翁建欣

(安徽师范大学数学计算机科学学院,安徽芜湖 241003)

运用同余及元素阶的性质,证明了对任意的正整数n,丢番图方程仅有正整数解(x,y,z)=(2,2,2).

Je´smanow icz猜想;丢番图方程;同余

DO I：10.3969/j.issn.1008-5513.2013.04.003

1 引言

2 引理及定理3的证明

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[5]Takafum iM iyazaki.Generalizations of classical resu lts on Je´smanow icz conjecture concerning Pythagorean trip les[J].Jou rnal of Num ber Theory.2013,133:583-595.

[6]Yang Zhijuan,Tang M in.On the Diophantine equation(8n)x+(15n)y=(17n)z[J].Bu ll.Aust.M ath. Soc.,2012,86(2):348-352.

[7]杨志娟,翁建欣.关于丢番图方程(12n)x+(35n)y=(37n)z[J].纯粹数学与应用数学,2012,28(5):698-704. [8]Tang M in,W eng Jianxin.Je´sm anow icz con jectu re revisited,II[EB/OL].(2013-04-02)[2013-05-20]

http://arxiv.org/pdf/1304.0514.pdf.

On the D iophan tine equation(195n)x+(28n)y=(197n)z

Ling Dengrong,Weng Jianxin
(School of Mathematics and Com puter Science,Anhui Normal University,Wuhu 241003)

In this paper,using the properties of congruences and the order of elements,we show that for any positive integer n,the Diophantine equation(195n)x+(28n)y=(197n)zhas no solution other than(x,y,z)= (2,2,2)in positive integers.

Je´smanow icz′con jecture,Diophantine equation,congruence

O156.4

A

1008-5513(2013)04-0342-08

2013-05-20.

国家自然科学基金(10901002);安徽省自然科学基金(1208085QA 02).

凌灯荣(1981-),硕士,讲师,研究方向：数论.

2010 M SC:11D 61