MathDB
L 2

Source:

May 25, 2007
number theorygreatest common divisorLinear Recurrences

Problem Statement

The Fibonacci sequence {Fn}\{F_{n}\} is defined by F1=1,  F2=1,  Fn+2=Fn+1+Fn.F_{1}=1, \; F_{2}=1, \; F_{n+2}=F_{n+1}+F_{n}. Show that gcd⁡(Fm,Fn)=Fgcd⁡(m,n)\gcd (F_{m}, F_{n})=F_{\gcd (m, n)} for all m,n∈Nm, n \in \mathbb{N}.
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