| 临界状态下的三项Diophantine方程 |
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| 引用本文： | 汤干文.临界状态下的三项Diophantine方程[J].数学杂志,2012,32(5):889-896. |
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| 作者姓名： | 汤干文 |
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| 作者单位： | 贺州学院数学系,广西贺州,542800 |
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| 摘 要： | 本文研究临界状态下三项Diophantine方程解的问题.运用无穷递降法证明了:设m,n,r是大于1的正整数,当1/m+1/n+1/r=1时,方程xm+yn=zn,min(x,y,z)>1,gcd(x,y)=1无正整数解(x,y,z).
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| 关 键 词： | 三项Diophantine方程 临界状态下 无穷递降法 |
THE TERNARY DIOPHANTINE EQUATION UNDER CRITICAL STATE |
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| TANG Gan-wen.THE TERNARY DIOPHANTINE EQUATION UNDER CRITICAL STATE[J].Journal of Mathematics,2012,32(5):889-896. |
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| Authors: | TANG Gan-wen |
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| Institution: | TANG Gan-wen(Department of Mathematics,Hezhou College,Hezhou 542800,China) |
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| Abstract: | In this paper,we study ternary Diophantine equation under critical state.By using the infinite descent method,we prove,let m,n,r be fixed positive integers large than one,that if 1/m + 1/n + 1/r = 1,then the equation xm+ yn = zn,min(x,y,z) > 1,gcd(x,y) = 1,has no positive integer solution(x,y,z). |
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| Keywords: | ternary diophantine equation critical state infinite descent method |
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