The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A058853 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A058853

Primes p such that x^43 = 2 has a solution mod p.
(history; published version)

#39 by Charles R Greathouse IV at Thu Sep 08 08:45:02 EDT 2022

PROG

(MAGMAMagma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^43 eq 2}]; // Vincenzo Librandi Sep 14 2012

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#38 by Peter Luschny at Tue Mar 09 19:15:09 EST 2021

STATUS

reviewed

approved

#37 by Peter Luschny at Tue Mar 09 12:13:20 EST 2021

STATUS

proposed

reviewed

#36 by Jianing Song at Tue Mar 09 04:48:38 EST 2021

STATUS

editing

proposed

Discussion

Tue Mar 09

12:12

Peter Luschny: There are so many beautiful conjectures in the OEIS 
which I am afraid will not be seen for years. 
I think we should announce them more proactive. By this I 
mean in places that are regularly read by research mathematicians.

12:12

Peter Luschny: In other words, I think you should put your conjecture as a question on MathOverflow.

#35 by Jianing Song at Tue Mar 09 04:48:27 EST 2021

COMMENTS

The generalized conjecture above is equivalent to: let P(p,1) be the set of primes congruent to 1 modulo p, P(p,1;a) be the set of primes q congruent to 1 modulo p such that x^p == a (mod q) has a solution, where p is a prime, a is not a p-th power, then the density of P(p,1;a) over P(p,1) is 1/p. - Jianing Song, Mar 09 2021

STATUS

approved

editing

#34 by Peter Luschny at Mon Mar 08 03:23:54 EST 2021

STATUS

reviewed

approved

#33 by Joerg Arndt at Mon Mar 08 02:31:04 EST 2021

STATUS

proposed

reviewed

#32 by Jianing Song at Mon Mar 08 00:13:47 EST 2021

STATUS

editing

proposed

#31 by Jianing Song at Mon Mar 08 00:13:02 EST 2021

COMMENTS

Primes not of the form 43n 43k + 1. - Charles R Greathouse IV, Aug 22 2011 [Not so! The smallest counterexample is 5419: 5419 = 43*126 + 1, but 2^43 == 2 (mod 5419), so it is here. - Jianing Song, Mar 07 2021]

This It is conjectured that this sequence has density 42/43 ~ 0.976744 over all the primes.

STATUS

approved

editing

Discussion

Mon Mar 08

00:13

Jianing Song: Sorry, it was meant to be a conjecture.

#30 by N. J. A. Sloane at Sun Mar 07 17:54:32 EST 2021

STATUS

proposed

approved