[seqfan] Re: A sequence connected with Wilson theorem

[Vladimir Shevelev]

Thank you, Mike. Unfortunately, an additional restriction (as x is prime), generally speaking,  "kills"
an important property of symmetry: x and p-1-x are both solutions or non-solutions.

Regards,
Vladimir

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Tw Mike [mt.kongtong at gmail.com]
Sent: 28 February 2014 16:04
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A sequence connected with Wilson theorem

Dear Vladimir,

Here's a seq based on your seq:

17, 97, 563, 613

Primes p,x and 1 < x < p -2  for x! + (p-1)!/x!==0 (mod p),x has only two
solutions.

and has only one solution:

7,     [1, 3, 5]
11,   [1, 5, 9]
47,   [1, 23, 45]
107, [1, 53, 105]
167, [1, 83, 165]
179, [1, 89, 177]
263, [1, 131, 261]
347, [1, 173, 345]
587, [1, 293, 585]
839, [1, 419, 837]

Yours mike,


2014-02-27 19:44 GMT+08:00 Vladimir Shevelev <shevelev at bgu.ac.il>:

> I have just submitted a sequence:"Primes p for which comparison x! +
> (p-1)!/x!==0 (mod p) has only two solutions 1<=x<=p-2 following from Wilson
> theorem: x = 1 and x = p-2" (A238460).
> The sequence begins 5,13,37,41,101,113,157,...
> Whether is another way to characterize these primes?
>
> Regards,
> Vladimir
>
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