A070188 - OEIS

A070188

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

113, 281, 353, 593, 617, 919, 1049, 1097, 1193, 1217, 1423, 1481, 1553, 1601, 1753, 1777, 1889, 1999, 2129, 2143, 2273, 2281, 2287, 2393, 2689, 2791, 2833, 3089, 3137, 3761, 3833, 4001, 4049, 4153, 4177, 4217, 4289, 4457, 4481, 4519, 4657, 4663, 4817

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..43.

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, ", "))))

(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

(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 */

CROSSREFS

Cf. A049544, A059667, A070179 - A070187.

Sequence in context: A142641 A070181 A001134 * A059331 A124586 A051110

Adjacent sequences: A070185 A070186 A070187 * A070189 A070190 A070191

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Apr 29 2002

STATUS

approved