| 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,2013,34(3):279~284 |
| 关于丢番图方程$x^y+y^x=z^z$ |
| On the Diophantine Equation $x^y+y^x=z^z$ |
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| DOI： |
| 中文关键词: 指数丢番图方程, 对数线性型, 素因子 |
| 英文关键词:Exponential Diophantine equations, Linear forms in logarithms,
Prime factor |
| 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) |
| Author Name | Affiliation | E-mail | | ZHANG Zhongfeng | School ofMathematics and Information Science, Zhaoqing University, Zhaoqing
526061, Guangdong, China | zh12zh31f@yahoo.com.cn; | | LUO Jiagui | School ofMathematics and Information Science, Zhaoqing University, Zhaoqing
526061, Guangdong, China | luojg62@yahoo.com.cn | | YUAN Pingzhi | School of Mathematics, South China Normal University, Guangzhou 510631,
China. | yuanpz@scnu.edu.cn |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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