| 关于指数Diophantine方程x2+by=cz |
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| 引用本文： | 乐茂华.关于指数Diophantine方程x2+by=cz[J].黑龙江大学自然科学学报,2005,22(5):681-684. |
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| 作者姓名： | 乐茂华 |
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| 作者单位： | 湛江师范学院,数学系,广东,湛江,524048 |
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| 基金项目： | SupportedbytheNationalNaturalScienceFoundationofChina(10271104)，theGuangdongProvincialNaturalScienceFounda-tion(04011425)，theNaturalScienceFoundationoftheEducationDepartmentofGuangdongProvince(0161) |
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| 摘 要： | 设m是偶数,r是奇数.设Ur,Vr是适合Vr+Ur-1=(m+-1)r的整数.证明了:当a=|Vr,|b=|Ur,|c=m2+1,r≡3(mod 4),m>r/π且m是2的方幂时,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 |
On the exponential diophantine equation x2 + by=cz |
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| LE Mao-hua.On the exponential diophantine equation x2 + by=cz[J].Journal of Natural Science of Heilongjiang University,2005,22(5):681-684. |
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| Authors: | LE Mao-hua |
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| Abstract: | Let m be an even integer, and let r be an odd integer. Let Ur, Vr be integers satisfying Vr +Ur(√-1)= (m+(√-1))r. It is shown that ifa = |Vr|, b= |Ur|, c=m2 +1,r≡3 (mod 4) andm is a power of 2 with m ＞ r/π, 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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