[seqfan] Re: Mod[Fibonacci[n],n^2]<=Mod[Fibonacci[n],n]

[zak seidov]

Indeed,
Mod[Fibonacci[n],n^2]=Mod[Fibonacci[n],n]=
{0, 1, 2, 3, 20, 61, 89, 144, 1365, 2003, 2584, 6765, 17711, 28657, 46368, 
121765, 196418, 282970, 317811, 514229, 832040}
for n=
{1, 2, 3, 4, 12, 45, 177, 1932, 2189, 4712, 5771, 5778, 43220, 288176, 
290422, 565181, 760763, 1244184, 1473817, 2842588, 2964627, 3100830}

Are these n's of any common feature?

--- On Fri, 4/30/10, Jay Anderson <horndude77 at gmail.com> wrote:

> From: Jay Anderson <horndude77 at gmail.com>
> Subject: [seqfan] Re: Mod[Fibonacci[n],n^2]<=Mod[Fibonacci[n],n]
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Friday, April 30, 2010, 12:53 AM
> On Thu, Apr 29, 2010 at 8:08 PM, zak
> seidov <zakseidov at yahoo.com>
> wrote:
> > 1.
> > Numbers n such that
> > Mod[Fibonacci[n],n^2]<=Mod[Fibonacci[n],n]
> > {1,2,3,4,12,45,177,1932,2189,4712,
> > 5771,5778,43220}
> > More terms?
> 
> [
>   1,
>   2,
>   3,
>   4,
>   12,
>   45,
>   177,
>   1932,
>   2189,
>   4712,
>   5771,
>   5778,
>   43220,
>   288176,
>   290422,
>   565181,
>   760763,
>   1244184,
>   1473817,
>   2842588,
>   2964627,
>   3100830,
> ]
> 
> Checked up through 5_000_000. I believe that
> Mod[Fibonacci[n],n^2]==Mod[Fibonacci[n],n] holds for all
> these so far.
> 
> 
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