| 关于指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z的正整数解(英文) |
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| 引用本文： | 何波,Togbe Alain. 关于指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z的正整数解(英文)[J]. 数学进展, 2011, 0(2) |
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| 作者姓名： | 何波 Togbe Alain |
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| 作者单位： | 阿坝师范高等专科学校数学系;普渡大学中北分校数学系; |
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| 基金项目： | supported by the Applied Basic Research Foundation of Sichuan Provincial Science and Technology Department(No.2009JY0091). |
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| 摘 要： | 本文通过计算Jacobi符号,运用代数数的对数线性型的下界估计,证明了:当整数a>1时,指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z仅有正整数解(x,y,z)=(2,1,1).
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| 关 键 词： | 指数丢番图方程 Jacobi符号 对数线性型 |
On the Positive Integer Solutions of the Exponential Diophantine Equation a~x +(3a~2 -1)~y =(4a~2 -1)~z |
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| HE bo,Togbe Alain. On the Positive Integer Solutions of the Exponential Diophantine Equation a~x +(3a~2 -1)~y =(4a~2 -1)~z[J]. Advances in Mathematics(China), 2011, 0(2) |
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| Authors: | HE bo Togbe Alain |
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| Affiliation: | HE bo~(1,*),Togbe Alain~(2,**) (1.Department of Mathematics,Aba Teachers College,Wenchuan,Sichuan,623000,P.R.China,2.Department of Mathematics,Purdue University North Central,1401,S.U.S.421,Westville,IN 46391,USA) |
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| Abstract: | In this paper,we use properties of the Jacobi symbol and lower bounds for linear forms in two logarithms of algebraic numbers to prove that the diophantine equation a~x +(3a~2-1)~y =(4a~2-1)~z has only the positive integer solution(x,y,z) =(2,1,1) for the integer a>1. |
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| Keywords: | exponential diophantine equations Jacobi symbols linear forms in the logarithms |
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