[seqfan] Re: More (composite) terms for A233281

franktaw at netscape.net franktaw at netscape.net
Tue Feb 11 21:11:34 CET 2014


The Fibonacci numbers that are a multiple of n, for any n, are 
precisely those whose index is a multiple of the index of the first 
such n. This is easy to see - just look at the Fibonacci numbers modulo 
n:  once you get a zero, it simply repeats, multiplied by a unit modulo 
n. E.g., mod 7 we have:

1 1 2 3 5 1 6 0
6 6 5 4 2 6 1 0
1 1 ...

Franklin T. Adams-Watters

-----Original Message-----
From: Hans Havermann <gladhobo at teksavvy.com>

I asked: "Does any prime factor of any composite Fibonacci number with 
prime
index appear as a prime factor for any *other* composite Fibonacci 
number with
prime index?"

Apparently this is well known (by those who know it well). Wikipedia 
says:
Fibonacci numbers that have a prime index do not share any common 
divisors
greater than 1 with the preceding Fibonacci numbers.

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