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Glasnik matematički, Vol. 38 No. 1, 2003.

Original scientific paper

Near squares in linear recurrence sequences

P. G. Walsh

Full text: english pdf 250 Kb

page 11-18

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cite

Abstract

Let T > 1 denote a positive integer. Let Un denote the linear recurrence sequence defined by U0 = 0, U1 = 1, and Uk+1 = 2TUk - Uk-1 for k 1. In recent years there have been some improvements on the determination of solutions to the Diophantine equation Un = cx2, where c is a given positive integer. In this paper we use a result of Bennett and the author to determine precisely the integer solutions to the related equation Un = cx2 1, where c is a given even positive integer.

Keywords

Linear recurrence sequence; diophantine equation; Pell equation

Hrčak ID:

1331

URI

https://hrcak.srce.hr/1331

Publication date:

1.6.2003.

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