#### 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

*e-mail:* `gwalsh@mathstat.uottawa.ca`

**Abstract.** Let *T* > 1 denote a positive integer.
Let *U*_{n} denote the
linear recurrence sequence defined by
*U*_{0} = 0, *U*_{1} = 1,
and *U*_{k+1} = 2*T**U*_{k}
- *U*_{k-1} for *k*
≥ 1.
In recent years there have
been some improvements on the determination of solutions to the
Diophantine equation *U*_{n} = *c**x*^{2},
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 *U*_{n} = *c**x*^{2}
± 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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