The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A040098

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A040098

Primes p such that x^4 = 2 has a solution mod p.
(history; published version)

#27 by Jon E. Schoenfield at Mon Feb 21 01:05:48 EST 2022

STATUS

editing

approved

#26 by Jon E. Schoenfield at Mon Feb 21 01:05:46 EST 2022

PROG

(MAGMAMagma) [ p: p in PrimesUpTo(919) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 2} ]; // Klaus Brockhaus, Dec 02 2008

STATUS

approved

editing

#25 by Bruno Berselli at Wed Jul 04 05:42:36 EDT 2018

STATUS

proposed

approved

#24 by Jon E. Schoenfield at Wed Jul 04 05:04:46 EDT 2018

STATUS

editing

proposed

#23 by Jon E. Schoenfield at Wed Jul 04 05:04:44 EDT 2018

LINKS

T. D. Noe, <a href="/A040098/b040098.txt">Table of n, a(n) for n = 1..1000</a>

PROG

(MAGMA) [ p: p in PrimesUpTo(919) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 2} ]; [From // _Klaus Brockhaus, _, Dec 02 2008]

(PARI) forprime(p=2, 2000, if([]~!=polrootsmod(x^4-2, p), print1(p, ", "))); print(); \\ _Joerg Arndt_, Jul 27 2011

/* Joerg Arndt, Jul 27 2011 */

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#22 by N. J. A. Sloane at Fri Apr 01 09:58:14 EDT 2016

STATUS

editing

approved

#21 by N. J. A. Sloane at Fri Apr 01 09:58:11 EDT 2016

CROSSREFS

For primes p such that x^m == 2 mod p has a solution for m = 2,3,4,5,6,7,... see A038873, A040028, A040098, A040159, A040992, A042966, ...

STATUS

approved

editing

#20 by Charles R Greathouse IV at Thu Nov 21 13:11:20 EST 2013

MATHEMATICA

ok[p_] := Reduce[ Mod[x^4 - 2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200]], ok] (* From _Jean-François Alcover, _, Dec 14 2011 *)

Discussion

Thu Nov 21

13:11

OEIS Server: https://oeis.org/edit/global/2066

#19 by Bruno Berselli at Thu Sep 13 16:51:34 EDT 2012

STATUS

proposed

approved

#18 by Vincenzo Librandi at Thu Sep 13 12:47:24 EDT 2012

STATUS

editing

proposed