- Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 26 Issue: 3
- All Solutions of the Diophantine Equations $2F_{n}=3^{s}⋅y^{b}$ and $F_{n}±1=3^{s}⋅y^{b}$
All Solutions of the Diophantine Equations $2F_{n}=3^{s}⋅y^{b}$ and $F_{n}±1=3^{s}⋅y^{b}$
Authors : İbrahim ERDURAN, Zafer ŞİAR
Pages : 488-492
Doi:10.16984/saufenbilder.1069960
View : 10 | Download : 4
Publication Date : 2022-06-30
Article Type : Other
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