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Lovely Fibonacci (Posted on 2013-05-11) Difficulty: 3 of 5
Let Fn be the nth Fibonacci number.

Prove: (Fmn-1) - (Fn-1)m is divisible by (Fn)2 for all m≥1 and n>1.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Counterexamples Comment 2 of 2 |
(In reply to Counterexamples by Jer)

Jer, your counter-example for the usual system seems to have a problem with it. In the standard numbering format for the sequence, F5 = 5, whereas you have considered it to be equal to 8. Setting F5 to the correct value of 5:

(F5) - (F2)^2 = 5 - 1^2 = 4 which IS divisible by (F3)^2 = 2^2 = 4.
  Posted by Justin on 2013-07-06 23:33:26

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