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Prove that [itex]f_{n}[/itex] is even if and only if n is divisible by 3. ([itex]f_{n}[/itex] is of course the nth Fibonacci number)

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Proving that n is divisible by 3 => [itex]f_{n}[/itex] is even is easily done by induction, but the other implication is eluding me. It is easy to show that [itex]f_{n}[/itex] is even iff [itex]f_{n-3}[/itex] is even, but I can't see if this helps. Any ideas about how to prove this implication? Thanks.