Glasnik matematički, Vol. 44 No. 1, 2009.
Izvorni znanstveni članak
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
Sažetak
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).
Ključne riječi
Goormaghtigh equation; continued fraction; congruence
Hrčak ID:
36942
URI
Datum izdavanja:
21.5.2009.
Posjeta: 1.228 *