Sums of Fibonacci numbers close to a power of 2
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Publication:6402725
DOI10.1007/S40590-023-00490-7arXiv2206.10356MaRDI QIDQ6402725
Publication date: 14 June 2022
Abstract: In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella-Peth"{o} version of the Baker-Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of Chern and Cui.
Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)
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