Glasnik Matematicki, Vol. 38, No.1 (2003), 11-18.
NEAR SQUARES IN LINEAR RECURRENCE SEQUENCES
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
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.
Key words and phrases. Linear recurrence sequence, diophantine equation, Pell
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