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.

(In reply to Observation by ed bottemiller)

There are 2 theorems concerning prime/composite relation
between Fibo series members and their indices.

You write: ..."Neither is asserting that if n is prime, then F(n) must be prime " to  which I'd like to add "and vice versa."

I believe one can EITHER  find the proofs on the WEB  OR work it out independently OR both.

 

Posted by Ady TZIDON on 2010-07-21 14:39:36