Fibonacci Proof

sirellwood · #1 $Old$ November 5th, 2009, 06:00 AM

Hi all

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

tonio · #2 $Old$ November 5th, 2009, 06:43 AM

Quote:

Originally Posted by sirellwood $View Post$

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.

sirellwood · #3 $Old$ November 5th, 2009, 09:08 AM

Sorry, im not sure where you are going with this one?