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Mathematical Citation Quotient (MCQ) 2017: 0.20

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On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers

Saúl Díaz Alvarado / Andrej Dujella / Florian Luca
Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0032


Here, we show that is the only solution in positive integers of the Diophantine equation

where is the mth Fibonacci number.

Keywords: Fibonacci Numbers; Applications of Lower Bounds for Linear Forms in Logarithms; Applications of the LLL Algorithm

About the article

Received: 2010-12-28

Accepted: 2011-09-17

Published Online: 2012-11-30

Published in Print: 2012-12-01

Citation Information: Integers, Volume 12, Issue 6, Pages 1127–1158, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0032.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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