| 关于丢番图方程$x^y+y^x=z^z$ |
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| 引用本文： | 张中峰,罗家贵,袁平之.关于丢番图方程$x^y+y^x=z^z$[J].数学年刊A辑(中文版),2013,34(3):279-284. |
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| 作者姓名： | 张中峰 罗家贵 袁平之 |
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| 作者单位： | 肇庆学院数学与信息科学学院, 广东 肇庆 526061.;华南师范大学数学科学学院, 广州 510631.;华南师范大学数学科学学院, 广州 510631. |
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| 基金项目： | 国家自然科学基金 (No.11271142)和广东省自然科学基金 (No.S2012040007653) |
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| 摘 要： | 利用$p$-adic对数线性型估计, 证明了方程x^y+y^x=z^z满足x,y,z均大于1的整数解(x,y,z)必然两两互素且有z<2.8*10^9.
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| 关 键 词： | 指数丢番图方程 对数线性型 素因子 |
On the Diophantine Equation $x^y+y^x=z^z$ |
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| ZHANG Zhongfeng,LUO Jiagui and YUAN Pingzhi.On the Diophantine Equation $x^y+y^x=z^z$[J].Chinese Annals of Mathematics,2013,34(3):279-284. |
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| Authors: | ZHANG Zhongfeng LUO Jiagui and YUAN Pingzhi |
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| Institution: | School ofMathematics and Information Science, Zhaoqing University, Zhaoqing
526061, Guangdong, China;School ofMathematics and Information Science, Zhaoqing University, Zhaoqing
526061, Guangdong, China;School of Mathematics, South China Normal University, Guangzhou 510631,
China. |
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| Abstract: | Let $x>1,\ y>1,\ z>1$ be
positive integer solutions of equation $x^y+y^x=z^z$. Using the linear
forms in $p$-adic logarithm, it is proved that $x,y,z$ are pairwise coprime integers and
$z<2.8\times 10^9$. |
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| Keywords: | Exponential Diophantine equations Linear forms in logarithms Prime factor |
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