Fibonacci and Lucas numbers close to Narayana's cows numbers

A. Satapathy; B.P. Tripathy; U.K. Dutta; B.K. Patel

doi:10.15421/242609

Fibonacci and Lucas numbers close to Narayana's cows numbers

A. Satapathy (School of Applied Sciences, KIIT University), https://orcid.org/0009-0006-2281-6379
B.P. Tripathy (School of Applied Sciences, KIIT University), https://orcid.org/0000-0001-6406-7560
U.K. Dutta (School of Applied Sciences, KIIT University), https://orcid.org/0000-0002-9112-955X
B.K. Patel (Government Women's College, Sambalpur University), https://orcid.org/0000-0001-7637-8489

Abstract

In this study, we find all Fibonacci and Lucas numbers which are close to Narayana's cows numbers. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella-Pethö version of the Baker-Davenport reduction method in Diophantine approximation.

Keywords

Fibonacci number; Lucas number; Narayana's cows number; linear forms in logarithms; reduction method

MSC 2020

11B39; 11J86

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