All Solutions of the Diophantine Equations $2F_{n}=3^{s}⋅y^{b}$ and $F_{n}±1=3^{s}⋅y^{b}$

Year 2022, Volume: 26 Issue: 3, 488 - 492, 30.06.2022

İbrahim Erduran , Zafer Şiar

https://doi.org/10.16984/saufenbilder.1069960

Abstract

The Fibonacci sequence 〖(F〗_n) is defined by F_0=0, F_1=1, and F_n=F_(n-1)+F_(n-2) for n≥2. In this paper, we will give all solutions of the Diophantine equations 2F_n=3^s∙y^b and F_n±1=3^s∙y^b in nonnegative integers s≥0, y≥1, b≥2, n≥1 and (3,y)=1.

Keywords

Fibonacci and Lucas numbers, Exponential Diophantine equations, Elementary number theory

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