journal6 ›› 2003, Vol. 24 ›› Issue (1): 1-4.

• 数学 •    下一篇

关于指数Diophantine方程的1个猜想

  

  1. (1.湛江师范学院数学系,广东 湛江 524048;2.上海师范大学数学系,上海 200234)
  • 出版日期:2003-03-15 发布日期:2012-11-09

A Conjecture Concerning an Exponential Diophantine Equation

  1. (1.Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China;2.Department of Mathematics,Shanghai Teachers’ Uniersity,Shanghai 200234,China)
  • Online:2003-03-15 Published:2012-11-09
  • About author:LE Mao-hua(1952-),male,was born in Shanghai City,professor of Department of Mathematics,Zhanjiang Normal College;research area is number theory.
  • Supported by:

    Supported by National Natural Science Foundation of China(19871073);Guangdong Provincial Natural Science Foundation(011871);Natural Science Foundation of the Education Department of Guangdong Province(0161)

摘要:设m,r是适合2|m,2r,r>1的正整数;Ur,Vr是适合Vr+Ur-1=(m+-1)r的整数;a,b,c是适合a=|Vr|,b=|Ur|,c=m2+1的正整数.证明了:如果b≡3(mod 4),b或c是素数,则方程x2+by=cz仅有正整数解(x,y,z)=(a,2,r).

关键词: 指数Diophantine方程, 解数, 上界

Abstract: Let m,r be positive integers such that 2|m,2r and r>1.let Ur,Vr be integers with Vr+Ur-1=(m+-1)r.Further let a,b,c be positive integers such that a=|Vr|,b=|Ur| and c=m2+1.It is proved that if b≡3(mod 4),and b or c is a prime,then the equation x2+by=cz has only the positive integer solution (x,y,z)=(a,2,r).

Key words: exponential diophantine equation, number of solutions, upper bound

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