[seqfan] Re: A069051 U A330382

[Tomasz Ordowski]

PS. The OEIS has almost everything,
namely "two in one, but minus one"...

Numbers n-1 such that 2^n == 2 (mod n-1) are A014741.

https://oeis.org/A014741

Prime numbers n are A069051.
Composite numbers n are A330382.

Conjecture:
2^(2^n-1) == 2 (mod 2^n-2)
if and only if 2^n == 2 (mod n-1).

Either proof or counterexample is welcome!


pon., 24 cze 2024 o 23:07 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

> Hello!
>
> How to prove that
> 2^(2^n-1) == 2 (mod 2^n-2)
> if and only if 2^n == 2 (mod n-1) ?
>
> Best,
>
> Tom Ordo
>
> https://oeis.org/A069051
> https://oeis.org/A330382
>
>