關于丟番圖方程(195n)x+(28n)y=(197n)z

凌燈榮,翁建欣

(安徽師范大學數學計算機科學學院,安徽蕪湖 241003)

關于丟番圖方程(195n)x+(28n)y=(197n)z

凌燈榮,翁建欣

(安徽師范大學數學計算機科學學院,安徽蕪湖 241003)

運用同余及元素階的性質,證明了對任意的正整數n,丟番圖方程僅有正整數解(x,y,z)=(2,2,2).

Je′smanow icz猜想;丟番圖方程;同余

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

1 引言

2 引理及定理3的證明

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[7]楊志娟,翁建欣.關于丟番圖方程(12n)x+(35n)y=(37n)z[J].純粹數學與應用數學,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.

國家自然科學基金(10901002);安徽省自然科學基金(1208085QA 02).

凌燈榮(1981-),碩士,講師,研究方向：數論.

2010 M SC:11D 61