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 : 24 | Download : 9

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :The Fibonacci sequence 〖insert ignore into journalissuearticles values(F〗_n); is defined by F_0=0, F_1=1, and F_n=F_insert ignore into journalissuearticles values(n-1);+F_insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(3,y);=1.
Keywords : Fibonacci and Lucas numbers, Exponential Diophantine equations, Elementary number theory