journal6 ›› 2001, Vol. 22 ›› Issue (1): 29-32.

• Mathematics • Previous Articles     Next Articles

The Exceptional Solutions of Goormaghtigh’s Equation (x3-1)/(x-1)=(yn-1)/(y- 1)

  

  1. ( Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524048, Guangdong China)
  • Online:2001-03-15 Published:2013-01-05

Abstract: In this paper we prove that the exceptional solutions ( x , y , n) of Goormaghtigh’s equation (x3-1)/(x-1)=(yn-1)/(y- 1) satisfy gcd( x , y ) > 1 and y |\x .

Key words: exponential diophantine equaton, Goormaghtigh&rsquo, s conjecture, exceptional solution

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