Prev: Frechet derivative in c0 space
Next: Total Object Mass is the cumulative sum of an object's atoms
From: Ludovicus on 16 Jul 2010 11:36
Conjecture or theorem?
"The set of prime numbers are divisors of the set
of Fibonacci numbers"
I found that the primes <=113 (Except 103),
are divisors of some of the Fibonacci's <= Fi(90).
Can anybody continue searching?
Ludovicus
From: bert on 16 Jul 2010 16:10
On 16 July, 16:36, Ludovicus <luir...(a)yahoo.com> wrote:
> Conjecture or theorem?
> "The set of prime numbers are divisors of  the set
> of Fibonacci numbers"
> I found that the primes <=113  (Except 103),
> are divisors of some of the Fibonacci's <= Fi(90).
> Can anybody continue searching?

According to Mathworld Wolfram, the Fibonacci
sequence is known (Wall 1960) to be periodic
modulo any integer, not just modulo a prime.
The Fibonacci sequence is reversible, so the
periodic values must include zero. Therefore
for any integer N, there are infinitely many
Fibonacci numbers - other than F[0] - whose
value is 0 modulo N.
--
From: Robert Israel on 16 Jul 2010 18:06

> On 16 July, 16:36, Ludovicus <luir...(a)yahoo.com> wrote:
> > Conjecture or theorem?
> > "The set of prime numbers are divisors of =A0the set
> > of Fibonacci numbers"
> > I found that the primes <=3D113 =A0(Except 103),
> > are divisors of some of the Fibonacci's <=3D Fi(90).
> > Can anybody continue searching?
>
> According to Mathworld Wolfram, the Fibonacci
> sequence is known (Wall 1960) to be periodic
> modulo any integer, not just modulo a prime.
> The Fibonacci sequence is reversible, so the
> periodic values must include zero. Therefore
> for any integer N, there are infinitely many
> Fibonacci numbers - other than F[0] - whose
> value is 0 modulo N.
> --


See OEIS sequence A001177 <http://www.research.att.com/~njas/sequences/A001177>.
BTW, a(103) = 104.
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
u
From: Tim Little on 16 Jul 2010 23:46
On 2010-07-16, Ludovicus <luiroto(a)yahoo.com> wrote:
> Conjecture or theorem?
> "The set of prime numbers are divisors of the set of Fibonacci
> numbers"

It is proven that for every prime there exists a Fibonacci number of
which it is a divisor, if that's what you mean.

For example, for all prime p>5 one of F(p+1) or F(p-1) will be a
multiple of p.


- Tim
 | 
Pages: 1
Prev: Frechet derivative in c0 space
Next: Total Object Mass is the cumulative sum of an object's atoms