Glasnik matematički, Vol. 44 No. 1, 2009.
Original scientific paper
https://doi.org/10.3336/gm.44.1.01
A remark on the Diophantine equation (x^3-1)/(x-1)=(y^n-1)/(y-1)
Bo He
; Sichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University
Abstract
In this remark, we use some properties of simple continued fractions of quadratic irrational numbers to prove that the equation
(x^3 - 1)/(x - 1) = (y^n - 1)/(y - 1), x, y, n in N, x > 1, y > 1, y > 3, n odd,
has only the solutions (x,y,n) = (5,2,5) and (90,2,13).
Keywords
Goormaghtigh equation; continued fraction; congruence
Hrčak ID:
36942
URI
Publication date:
21.5.2009.
Visits: 1.203 *