Geodesic
On the $X$-coordinates of Pell equations which are Tribonacci numbers
Florian Luca1 ; Amanda Montejano2 ; Laszlo Szalay3 ; Alain Togbé4
1 School of Mathematics University of the Witwatersrand Private Bag X3 Wits 2050, South Africa and Department of Mathematics Faculty of Science University of Ostrava 30. dubna 22 701 03 Ostrava 1, Czech Republic
2 Facultad de Ciencias UNAM Campus Juriquilla Juriquilla, Mexico
3 Department of Mathematics and Informatics J. Selye University Hradna ul. 21 94501 Komarno, Slovakia
4 Department of Mathematics, Statistics and Computer Science Purdue University Northwest 1401 S, U.S. 421 Westville, IN 46391, U.S.A.
Acta Arithmetica, Tome 179 (2017) no. 1, pp. 25-35 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 value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=\pm 1$ which is a Tribonacci number, with a few exceptions that we completely characterize.
DOI : 10.4064/aa8553-2-2017
Keywords: integer geq which square there value positive integer participating pell equation dy which tribonacci number few exceptions completely characterize

Florian Luca 1 ; Amanda Montejano 2 ; Laszlo Szalay 3 ; Alain Togbé 4

1 School of Mathematics University of the Witwatersrand Private Bag X3 Wits 2050, South Africa and Department of Mathematics Faculty of Science University of Ostrava 30. dubna 22 701 03 Ostrava 1, Czech Republic
2 Facultad de Ciencias UNAM Campus Juriquilla Juriquilla, Mexico
3 Department of Mathematics and Informatics J. Selye University Hradna ul. 21 94501 Komarno, Slovakia
4 Department of Mathematics, Statistics and Computer Science Purdue University Northwest 1401 S, U.S. 421 Westville, IN 46391, U.S.A. 
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     author = {Florian Luca and Amanda Montejano and Laszlo Szalay and Alain Togb\'e},
     title = {On the $X$-coordinates of {Pell} equations which are {Tribonacci} numbers},
     journal = {Acta Arithmetica},
     pages = {25--35},
     year = {2017},
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     number = {1},
     doi = {10.4064/aa8553-2-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8553-2-2017/}
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Florian Luca; Amanda Montejano; Laszlo Szalay; Alain Togbé. On the $X$-coordinates of Pell equations which are Tribonacci numbers. Acta Arithmetica, Tome 179 (2017) no. 1, pp. 25-35. doi: 10.4064/aa8553-2-2017

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