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Fibo composes (Posted on 2010-07-21) Difficulty: 4 of 5
Fibonacci sequence is defined by f(1)=1,f(2)=1 and f(m) =f(m-1)+f(m-2) i.e. 1, 1, 2, 3, 5, 8, 13, ...
Prove that for all composite values of n>4, f(n) is composite.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.6667 (3 votes)

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Observation | Comment 1 of 6

Ady's new problem seems to ask for proof that IF index n is composite (i.e. not prime), THEN F(n) is also composite (not prime).  This seems the contrapositive formulatiion of Carmichael's theorem that IF F(n) is prime (not composite) THEN index n must be prime (not composite) -- with the same restriction to exclude F(4)=3, in all cases.  Neither is asserting that if n is prime, then F(n) must be prime -- which is in any case false (e.g. F(19)=4181=37*113.)  Is there another twist?

 

 


  Posted by ed bottemiller on 2010-07-21 14:00:52
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