Geodesic
On the $x$-coordinates of Pell equations which are Fibonacci numbers II
Bir Kafle 1   ; Florian Luca 2   ; Alain Togbé 1
1 Mathematics Department Purdue University Northwest 1401 S, U.S. 421 Westville, IN 46391, U.S.A.
2 School of Mathematics University of the Witwatersrand Private Bag X3 Wits 2050, South Africa and Max Planck Institute for Mathematics Vivatgasse 7 53111 Bonn, Germany
Colloquium Mathematicum, Tome 149 (2017) no. 1, pp. 75-85 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For an integer $d\geq 2$ which is not a square, we show that there is at most one positive integer $x$ appearing in a solution of the Pell equation $x^2-dy^2=\pm 4$ which is a Fibonacci number, except when $d=2, 5$, where we have exactly two values of $x$ being members of the Fibonacci sequence.
DOI : 10.4064/cm6960-8-2016
Keywords: integer geq which square there positive integer appearing solution pell equation dy which fibonacci number except where have exactly values being members fibonacci sequence

Bir Kafle  1   ; Florian Luca  2   ; Alain Togbé  1

1 Mathematics Department Purdue University Northwest 1401 S, U.S. 421 Westville, IN 46391, U.S.A.
2 School of Mathematics University of the Witwatersrand Private Bag X3 Wits 2050, South Africa and Max Planck Institute for Mathematics Vivatgasse 7 53111 Bonn, Germany 
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     title = {On the $x$-coordinates of {Pell} equations which are {Fibonacci} numbers {II}},
     journal = {Colloquium Mathematicum},
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Bir Kafle; Florian Luca; Alain Togbé. On the $x$-coordinates of Pell equations which are Fibonacci numbers II. Colloquium Mathematicum, Tome 149 (2017) no. 1, pp. 75-85. doi: 10.4064/cm6960-8-2016

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