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On Indefinite Equation(x3-31)/(x-1)=(yn-1)/(y-1)(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2013年03期
Page:
13-15
Research Field:
数学
Publishing date:

Info

Title:
On Indefinite Equation(x3-31)/(x-1)=(yn-1)/(y-1)
Author(s):
Guan Xungui
School of Mathematics,Physics and Information Science,Taizhou University,Taizhou 225300,China
Keywords:
exponential indefinite equation; Goormaghtigh’s conjecture; exceptional solution
PACS:
O156.1
DOI:
-
Abstract:
This paper proved that if(x,y,n)is an exceptional solution of indefinite equation(x3-31)/(x-1)=(yn-1)/(y-1)with n≥3·22r-4-241 and 2n,then y<2n-r and x<2(n2-(r+-(r+1)n+r+2)/22122,where r>1 be integer.

References:

[1]Goormaghtigh R.L’Intermediaire Des Mathématiciens[M].Paris:Gauthier-Vallars,1917:88.
[2]Nesterenko Y V,Shorey T N.On an equation of Goormaghtigh[J].Acta Arith,1998,83:381-389.
[3]乐茂华.关于Goormaghtigh方程(x3-1)/(x-1)=(yn-1)/(y-1)[J].数学学报,2002,45(3):505-508.
[4]苟素,王婷婷.一类不定方程及其素数解[J].陕西师范大学学报:自然科学版,2011,39(3):20-22.

Memo

Memo:
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Last Update: 2013-09-30