Talk:Fibonacci number

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Revision as of 16:23, 30 December 2007 by imported>Wlodzimierz Holsztynski (→‎Fibonacci number and Primenumber: exception F_4 = 3)
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 Definition Element of the sequence in which the first number is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers. [d] [e]
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Fibonacci number and Primenumber

  • If   is a prime number then   is prime. (The converse is false.)

is not correct:

n F(n)
0 0
1 1
2 1
3 2
4 3
5 5

The forth Fibonacci number is 3. 3 is a Primenumber, but 4 is not a Primenumber. --arbol01 07:30, 30 December 2007 (CST)

True. This is the only exception, due to the fact that 4=2*2 while F_2=1 is not greater than 1. Thus for the composite number 4=n=a*b=2*2 we do not get a proper divisor of F_a | F_n, i.e. F_2 | F_4, because F_2 is not proper, it is equal 1. It was my fault to overlook this case; I was happy (too happy) to see that the general theorem works accidentally also for prime F_3=2, where the index is prime 3. Thank you, Wlodzimierz Holsztynski 16:23, 30 December 2007 (CST)