Original scientific paper

https://doi.org/10.3336/gm.48.2.04

On a Diophantine equation of Andrej Dujella

Keith R. Matthews orcid.org/0000-0002-9564-1702 ; Department of Mathematics, University of Queensland, Brisbane, Australia, 4072 and Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, Australia, 0200

Abstract

We investigate positive solutions (x,y) of the Diophantine equation x2-(k2+1)y2=k2 that satisfy y < k-1, where k≥ 2. It has been conjectured that there is at most one such solution for a given k.

Keywords

Quadratic diophantine equations; continued fractions

Hrčak ID:

112208

URI

https://hrcak.srce.hr/112208

Publication date:

16.12.2013.

Visits: 1.351 *