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On the $x$-coordinates of Pell equations which are Fibonacci numbers

Florian Luca, Alain Togbé

Abstract


For an integer $d>2$ which is not a square, we show that there is at most one value of the positive integer $x$ participating in the Pell equation $x^2-dy^2=\pm 1$ which is a Fibonacci number.


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References


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DOI: http://dx.doi.org/10.7146/math.scand.a-97271

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