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- Title
ON PILLAI'S PROBLEM WITH LUCAS NUMBERS AND POWERS OF 3.
- Authors
Edjeou, Bilizimbéyé; Tall, Amadou; Ben Fraj Ben Maaouia, Mohamed
- Abstract
In this paper, we find all integers m having at least two representations as a difference between a Lucas number and a power of 3. The sequence of Lucas numbers, (Lk)k≥0, is given by L0 = 2,L1 = 1 and Lk+2 = Lk+1 + Lk, for k &#8805l; 0. The tools used to solve our main theorem are linear forms in logarithms, properties of continued fractions and a version of the Baker-Davenport reduction method in Diophantine approximation.
- Subjects
LUCAS numbers; DIOPHANTINE approximation; CONTINUED fractions; INTEGERS; LOGARITHMS
- Publication
Integers: Electronic Journal of Combinatorial Number Theory, 2021, Vol 21, p1
- ISSN
1553-1732
- Publication type
Article