Question

Hi, can somebody help me prove this \(\forall n \in \mathbb{N}: gcd(f_{n+1},f_{n})=1\), where \(\{ f_{n} \} _{n=0}^\infty\) is the fibonacci sequence?

Answer 1

gcd is greatest common divisor

Answer 2

Have you considered a proof by induction?

Answer 3

Doing so shouldn't be too difficult. Use the fact that for two natural numbers \(a,b\), you have \(\gcd(a,b)=\gcd(a+b,b).\)