[seqfan] Re: A question on sequence A174407

[Sean A. Irvine]

Hi José,

I get the existing terms.

It is the number of distinct "g" not the number of distinct "x" that
matters.

Sean.


On Tue, 16 Apr 2024 at 06:19, José Hdz. Stgo. via SeqFan <
seqfan at list.seqfan.eu> wrote:

> Dear all,
>
> Would any of you be so kind as to take a look at the COMMENTS section of
> entry A174407?
>
> For instance, according to this sequence's definition, the number of
> primitive roots g (modulo 17) such that g^x = x (mod 17) for some integer x
> is 7.
>
> If I understand correctly, the first sentence in the COMMENTS implies that
> a(7) should coincide with "the number of x with 0<x<17 and g^x = x (mod
> 17)".
>
> I wrote a Mathematica program to output all of the x in (0, 17) such that
> g^x = x (mod 17) for a primitive root g (modulo 17). I only obtained 6
> (distintc) such x's whereas the entry is asserting the existence of 7 such
> x's.
>
> Would you be so kind as to take a look at this potential issue? Here you
> can find the code of the aforementioned program:
>
> p=17;
> For[g = 1, g < p, g++,
> If[MultiplicativeOrder[g, p] == p - 1, x = 1;
> While[x < p,
> If[Mod[g^x - x, p] == 0, Print[x, ",", g]; x = x + 1, x = x + 1]]]]
>
> Please, let me thank you in advance for your attentive reply.
>
> Best regards,
>
> José Hdz. Stgo.
>
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