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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


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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

https://hrcak.srce.hr/36942

Publication date:

21.5.2009.

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