Original scientific paper

https://doi.org/10.3336/gm.55.1.01

On Y-coordinates of Pell equations which are base 2 rep-digits

Bernadette Faye-Fall ; UFR SAT, Université Gaston Berger , Saint-Louis 32002, Sénégal
Florian Luca orcid.org/0000-0003-1321-4422 ; School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa, and Research Group in Algebraic Structures and Applications, King Abdulaziz University, Jeddah, Saudi Arabia, and Centro de Ciencias Matemáticas

Abstract

In this paper, we show that if (Xk,Yk) is the kth solution of the Pell equation X2-dY2=1 for some non-square integer d>1, then the equation Yk=2n-1 has at most two positive integer solutions (k,n).

Keywords

Pell equations; exponential Diophantine equations; applications of linear forms in logarithms

Hrčak ID:

239038

URI

https://hrcak.srce.hr/239038

Publication date:

12.6.2020.

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