Glasnik Matematicki, Vol. 38, No.1 (2003), 11-18.


P. G. Walsh

Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, Ontario, Canada K1N-6N5

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.

2000 Mathematics Subject Classification.   11D25, 11B39.

Key words and phrases.   Linear recurrence sequence, diophantine equation, Pell equation.

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