Glasnik matematički, Vol. 55 No. 1, 2020.
Izvorni znanstveni članak
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
Sažetak
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).
Ključne riječi
Pell equations; exponential Diophantine equations; applications of linear forms in logarithms
Hrčak ID:
239038
URI
Datum izdavanja:
12.6.2020.
Posjeta: 777 *