| On the Diophantine System a^2 ＋ b^2 = c^3 and a^x ＋ b^y = c^z for b is an Odd Prime |
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| 引用本文： | Mao Hua LE. On the Diophantine System a^2 ＋ b^2 = c^3 and a^x ＋ b^y = c^z for b is an Odd Prime[J]. 数学学报(英文版), 2008, 24(6): 917-924. DOI: 10.1007/s10114-007-6140-x |
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| 作者姓名： | Mao Hua LE |
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| 作者单位： | Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524048, P. R. China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10271104） and the Guangdong Provincial Natural Science Foundation （No. 04011425） |
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| 摘 要： | Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 ＋ b^2 = c^3 and b is an odd prime, then the equation a^x ＋ b^y = c^z has only the positive integer solution （x, y, z） = （2,2,3）.
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| 关 键 词： | 数论 丢番图方程 正整数解 广义费马推论 |
On the diophantine system a 2 + b 2 = c 3 and a x + b y = c z for b is an odd prime |
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| Mao Hua Le. On the diophantine system a 2 + b 2 = c 3 and a x + b y = c z for b is an odd prime[J]. Acta Mathematica Sinica(English Series), 2008, 24(6): 917-924. DOI: 10.1007/s10114-007-6140-x |
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| Authors: | Mao Hua Le |
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| Affiliation: | (1) Department of Mathematics, Zhanjiang Normal College, Zhanjiang, 524048, P. R. China |
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| Abstract: | Let a, b and c be fixed coprime positive integers. In this paper we prove that if a 2 + b 2 = c 3 and b is an odd prime, then the equation a x + b y = c z has only the positive integer solution (x, y, z) = (2, 2, 3). Supported by the National Natural Science Foundation of China (No. 10271104) and the Guangdong Provincial Natural Science Foundation (No. 04011425) |
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| Keywords: | exponential diophantine equation positive integer solution generalized Fermat conjecture |
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