On the Diophantine equation $F_{n}-F_{m}=2^{a}$
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 119-126
MSC: 11B39, 11J86, 11D61.
DOI: 10.4064/cm7485-12-2018
Published online: 25 October 2019
Abstract
We solve the Diophantine equation in the tittle in nonnegative integers $m,n,$ and $a$. In order to prove our result, we use lower bounds for linear forms in logarithms and a version of the Baker–Davenport reduction method in Diophantine approximation.
