关于丢番图方程(12n)x+(35n)y=(37n)z

杨志娟,翁建欣

(安徽师范大学数学系,安徽 芜湖 241003)

关于丢番图方程(12n)x+(35n)y=(37n)z

杨志娟,翁建欣

(安徽师范大学数学系,安徽 芜湖 241003)

运用同余及元素阶的性质,证明对任意正整数n,丢番图方程

仅有正整数解(x,y,z)=(2,2,2).

Je´smanowicz猜想;丢番图方程;同余

1 引言

2 引理及定理 4的证明

致谢感谢导师汤敏教授在论文撰写过程中给予的精心指导.

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On the Diophantine equation(12n)x+(35n)y=(37n)z

Yang Zhijuan,Weng Jianxin
(School of Mathematics and Computer Science,Anhui Normal University,Wuhu 241003,China)

Using the properties of congruences and the order of elements,we show that,for any positive integer n,the Diophantine equation(12n)x+(35n)y=(37n)zhas no solution other than(x,y,z)=(2,2,2)in positive integers.

Je´smanowicz conjecture,Diophantine equation,congruence

O156

A

1008-5513(2012)05-0698-07

2012-05-14.

国家自然科学基金(10901002);安徽省自然科学基金(1208085QA02).

杨志娟(1987-),硕士生,研究方向：组合数论.

2010 MSC:11D61