Glasnik matematički, Vol. 41 No. 2, 2006.
Izvorni znanstveni članak
On a family of quatric equations and a Diophantine problem of Martin Gardner
P. G. Walsh
Sažetak
Wilhelm Ljunggren proved many fundamental theorems on equations of the form aX^2 - bY^4 = δ, where δ ∈ {±1, 2, ±4}. Recently, these results have been improved using a number of methods. Remarkably, the equation aX^2 - bY^4 = -2 remains elusive, as there have been no results in the literature which are comparable to results proved for the other values of δ. In this paper we give a sharp estimate for the number of integer solutions in the particular case that a = 1 and b is of a certain form. As a consequence of this result, we give an elementary solution to a Diophantine problem due to Martin Gardner which was previously solved by Charles Grinstead using Baker's theory.
Ključne riječi
Diophantine equation; integer point; elliptic curve; Pell equation
Hrčak ID:
5847
URI
Datum izdavanja:
9.12.2006.
Posjeta: 1.614 *