# [seqfan] Re: A strong question

Tomasz Ordowski tomaszordowski at gmail.com
Tue Nov 27 19:00:58 CET 2018

```P.S. See my drafts:

https://oeis.org/draft/A322120
and
https://oeis.org/draft/A322121

Thomas Ordowski

niedz., 25 lis 2018 o 18:57 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

> Dear SeqFans!
>
> Let's define:
>
> Composite numbers m such that b^(m-1) == 1 (mod (b^2-1)m) has a solution
> b.
>
> 25, 49, 65, 85, 91, 121, 125, 133, 145, 169, 185, 205, 217, 221, 247, 259,
> ...
>
> Note: If such m exists, then the smallest b is in the range 2 <= b <= m-2.
>
> Conjecture:
> If m is a composite number such that b^(m-1) == 1 (mod (b^2-1)m) for some
> b,
> then m is a strong pseudoprime to some base a in the range 2 <= a <= m-2.
>
> Note that not always the smallest a = b.
>
> The question: Is this a proper subset of A181782 ?
>
> Are my pseudoprimes stronger than the strong pseudoprimes?
>
> Cf. https://oeis.org/A181782 (strong pseudoprimes to some base).
>
> Best regards,
>
> Thomas Ordowski
>
> P.S. Let a(n) be the smallest composite k such that n^(k-1) == 1 (mod
> (n^2-1)k), for n > 1.
>
> 341, 91, 91, 217, 481, 25, 65, 91, 91, 133, 133, 85, 781, 341, 91, 91, 25,
> 49, 671, 221, 169, ...
>
> The sequence is not in OEIS.
>

```