[seqfan] Re: A question on sequence A174407

[Tim Peters]

It would have helped a bit if you showed your output. I don't speak
Mathematica, but I found 7 without it.

3^5 = 5 (mod 17)
5^11 = 11 (mod 17)
6^2 = 2 (mod 17)
7^3 = 3 (mod 17)
10^4 = 4 (mod 17)
11^2 = 2 (mod 17)
12^7 = 7 (mod 17)

Here's a Python statement verifying the above:

assert all(pow(b, e, 17) == e
           for b, e in [(3, 5), (5, 11), (6, 2),
                        (7, 3), (10, 4), (11, 2),
                        (12, 7)])

The only primitive root of 17 that didn't have a fixed point was 14.

On Mon, Apr 15, 2024 at 1:19 PM 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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