On a diophantine equation of Andrej Dujella

Keith R. Matthews; John P. Robertson; Jim White

doi:10.3336/gm.48.2.04

On a diophantine equation of Andrej Dujella

Keith R. Matthews
, John P. Robertson
, Jim White

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	265-289
Number of pages	25
Journal	Glasnik Matematicki
Volume	48
Issue number	2
DOIs	https://doi.org/10.3336/gm.48.2.04
Publication status	Published - 2013

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title = "On a diophantine equation of Andrej Dujella",

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 = "Continued fractions, Quadratic diophantine equations",

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AU - Robertson, John P.

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AB - 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.

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KW - Quadratic diophantine equations

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DO - 10.3336/gm.48.2.04

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On a diophantine equation of Andrej Dujella

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