- Problem Statement
- Let ##F_n be the n-th Fibonacci number, where F_0=0 and F_1=1. Prove that if n is a multiple of 4, the F_n is a multiple of 3.

- Relevant Equations
- ##F_{4k+4}

Can somebody please explain below

##F_{4k+4} = F_{4k+3} + F_{4k+2}##

I thought it would be

##F_{4k+4} = F_{4k+3} +F_{4k+1}##

Thanks!

##F_{4k+4} = F_{4k+3} + F_{4k+2}##

I thought it would be

##F_{4k+4} = F_{4k+3} +F_{4k+1}##

Thanks!