# Fibonacci Proof

• Nov 5th 2009, 05:00 AM
sirellwood
Fibonacci Proof
Hi all

Prove that every 4th Fibonacci number is divisible by 3, that is 3|f4n, for all n>=1.
• Nov 5th 2009, 05:43 AM
tonio
Quote:

Originally Posted by sirellwood
Hi all

Prove that every 4th Fibonacci number is divisible by 3, that is 3|f4n, for all n>=1.

Induction and some patience: $F_{4n}=F_{4n-1}+F_{4n-2}=F_{4n-2}+F_{4n-3}+F_{4n-3}+F_{4n-4}$ $= F_{4n-3}+F_{4n-4}+F_{4n-3}+F_{4n-3}+F_{4n-4}=...$

Tonio

Pd. The solution's already present in the rightmost expression above.
• Nov 5th 2009, 08:08 AM
sirellwood
Sorry, im not sure where you are going with this one?