A Conjecture Concerning an Exponential Diophantine Equation

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

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A Conjecture Concerning an Exponential Diophantine Equation

(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)

Abstract

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

LE Mao-Hua. A Conjecture Concerning an Exponential Diophantine Equation[J]. journal6, 2003, 24(1): 1-4.

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A Conjecture Concerning an Exponential Diophantine Equation

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