Powers of Two as Sums of Two Lucas Numbers
Jhon J. Bravo
University of Cauca
Street 5 No. 4-70
School of Mathematics
University of the Witwatersrand
P. O. Box Wits 2050
Santiago de Querétaro 76230
Querétaro de Arteaga
Let (Ln)n ≥ 0
be the Lucas sequence given by L0 = 0,
L1 = 1,
and Ln+2 =
Ln for n ≥ 0.
In this paper, we are interested in finding all
powers of two which are sums of two Lucas numbers, i.e., we study the
Lm = 2a
in nonnegative integers
n, m, and a.
The proof of our main theorem uses lower bounds for linear forms in
logarithms, properties of continued fractions, and a version of the
Baker-Davenport reduction method in diophantine approximation. This
paper continues our previous work where we obtained a similar result
for the Fibonacci numbers.
Full version: pdf,
(Concerned with sequences
Received March 17 2014;
revised versions received July 22 2014; July 30 2014.
Published in Journal of Integer Sequences, July 30 2014.
Journal of Integer Sequences home page