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Fibonacci sequence, division

  1. Nov 12, 2006 #1
    Here is the question:
    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)

    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.
  2. jcsd
  3. Nov 12, 2006 #2
    If this is easy to show, then it would be enough to look at the evenness of [tex]f_0, f_1[/tex], and [tex]f_2[/tex].
  4. Nov 12, 2006 #3
    I was thinking about that, and I think you are absolutely right. Thanks.
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