On the Diophantine equation $F_{n}-F_{m}=2^{a}$

Zafer Şiar; Refik Keskin

doi:10.4064/cm7485-12-2018

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

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On the Diophantine equation $F_{n}-F_{m}=2^{a}$

Volume 159 / 2020

Zafer Şiar, Refik Keskin 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.

Authors

Zafer ŞiarDepartment of Mathematics
Bingöl University
Bingöl, Turkey
e-mail
Refik KeskinDepartment of Mathematics
Sakarya University
Sakarya, Turkey
e-mail

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Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

Colloquium Mathematicum

On the Diophantine equation F_{n}-F_{m}=2^{a}

Volume 159 / 2020

Abstract

Authors

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On the Diophantine equation $F_{n}-F_{m}=2^{a}$