Glasnik Matematicki, Vol. 55, No. 1 (2020), 1-12.

ON Y-COORDINATES OF PELL EQUATIONS WHICH ARE BASE 2 REP-DIGITS

Bernadette Faye-Fall and Florian Luca

UFR SAT, Université Gaston Berger , Saint-Louis 32002, Sénégal
e-mail: bernadette.fayee@gmail.com

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, UNAM, Morelia, Mexico
e-mail: florian.luca@wits.ac.za

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).

2010 Mathematics Subject Classification.   11B39, 11D61

Key words and phrases.   Pell equations, exponential Diophantine equations, applications of linear forms in logarithms

Full text (PDF) (free access)

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

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