| 关于指数Diophantine方程的1个猜想 |
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| 引用本文： | 乐茂华.关于指数Diophantine方程的1个猜想[J].吉首大学学报(自然科学版),2003,24(1):1-4. |
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| 作者姓名： | 乐茂华 |
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| 作者单位： | (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) |
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| 基金项目： | SupportedbyNationalNaturalScienceFoundationofChina(198710 73 )，GuangdongProvincialNaturalScienceFoundation(0 11871)，NaturalScienceFoundationoftheEducationDepartmentofGuangdongProvince(0 161) |
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| 摘 要： | 设m,r是适合2｜m，2r，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）.
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| 关 键 词： | 指数Diophantine方程 解数 上界 |
A Conjecture Concerning an Exponential Diophantine Equation |
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| Abstract.A Conjecture Concerning an Exponential Diophantine Equation[J].Journal of Jishou University(Natural Science Edition),2003,24(1):1-4. |
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| Authors: | Abstract |
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| Institution: | (1.Department of Mathematics，Zhanjiang Normal College,Zhanjiang 524048,Guangdong China;2.Department of Mathematics，Shanghai Teachers’ Uniersity,Shanghai 200234,China) |
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| 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 .Fur-ther 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 aprime,then the equation x2 + by = cz has only the positive integer solution ( x, y ,z) = (a,2,r). |
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| Keywords: | exponential diophantine equation number of solutions upper bound |
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