The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A070188 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A070188

Primes p such that x^12 = 2 has a solution mod p, but x^(12^2) = 2 has no solution mod p.
(history; published version)

#11 by Charles R Greathouse IV at Thu Sep 08 08:45:05 EDT 2022

PROG

(MAGMAMagma) [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^144 eq 2} and exists{x: x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 21 2012

Discussion

Thu Sep 08

08:45

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

#10 by Joerg Arndt at Fri Sep 21 02:52:03 EDT 2012

STATUS

reviewed

approved

#9 by Bruno Berselli at Fri Sep 21 02:47:00 EDT 2012

STATUS

proposed

reviewed

#8 by Joerg Arndt at Fri Sep 21 02:41:28 EDT 2012

STATUS

editing

proposed

#7 by Joerg Arndt at Fri Sep 21 02:41:22 EDT 2012

PROG

(PARI)

ok(p, r, k1, k2)={

if ( Mod(r, p)^((p-1)/gcd(k1, p-1))!=1, return(0) );

if ( Mod(r, p)^((p-1)/gcd(k2, p-1))==1, return(0) );

return(1);

}

forprime(p=2, 10^5, if (ok(p, 2, 12, 12^2), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

STATUS

proposed

editing

#6 by Vincenzo Librandi at Fri Sep 21 02:21:29 EDT 2012

STATUS

editing

proposed

#5 by Vincenzo Librandi at Fri Sep 21 02:21:24 EDT 2012

PROG

(MAGMA) [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^144 eq 2} and exists{x: x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 21 2012

KEYWORD

nonn,easy

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 17:27:35 EDT 2012

AUTHOR

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Apr 29 2002

Discussion

Fri Mar 30

17:27

OEIS Server: https://oeis.org/edit/global/145

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

OFFSET

0,1,1

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

PROG

(PARI) forprime(p=2, 5000, x=0; while(x<p&&x^12%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(12^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))

KEYWORD

nonn,new

nonn