| A Conjecture Concerning the Pure Exponential Diophantine Equation a^x ＋ b^y = c^z |
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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, Zhanfiang 524005, P. R. China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No.10271104）, the Guangdong Provincial Natural Science Foundation （No.011781） and the Natural Science Foundation of the Education Department of Guangdong Province （No.0161） |
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| 摘 要： | Let a, b, c, r be fixed positive integers such that a^2 ＋ b^2 = c^r, min（a, b, c, r） 〉 1 and 2 r. In this paper we prove that if a ≡ 2 （mod 4）, b ≡ 3 （mod 4）, c 〉 3.10^37 and r 〉 7200, then the equation a^x ＋ b^y = c^z only has the solution （x, y, z） = （2, 2, r）.
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| 关 键 词： | 纯指数丢番图方程 数字解 正整数 确定性 |
| 收稿时间： | 2002-10-10 |
| 修稿时间： | 2002-10-102003-08-06 |
A Conjecture Concerning the Pure
Exponential Diophantine Equation a
x
+ b
y
= c
z |
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| Mao Hua LE.A Conjecture Concerning the Pure
Exponential Diophantine Equation a
x
+ b
y
= c
z[J].Acta Mathematica Sinica,2005,21(4):943-948. |
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| Authors: | Mao Hua Le |
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| Institution: | (1) Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524005, P. R. China |
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| Abstract: | Let a, b, c, r be fixed positive integers such that a
2 + b
2 = c
r
, min(a, b, c, r) > 1 and 2 ∤ r. In
this paper we prove that if a ≡ 2 (mod 4), b ≡ 3 (mod 4), c > 3.1037 and r > 7200, then the equation
a
x
+ b
y
= c
z
only has the solution (x, y, z) = (2, 2, r).
Supported by the National Natural Science Foundation of China (No. 10271104), the Guangdong Provincial
Natural Science Foundation (No. 011781) and the Natural Science Foundation of the Education Department of
Guangdong Province (No. 0161) |
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| Keywords: | Pure exponential diophantine equation Number of solutions Completely determine |
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