A070180 Primes p such that x^3 = 2 has a solution mod p, but x^(3^2) = 2 has no solution mod p.

109, 307, 433, 739, 811, 919, 1423, 1459, 1999, 2017, 2143, 2179, 2251, 2287, 2341, 2791, 2917, 2953, 3061, 3259, 3331, 3457, 3889, 4177, 4339, 4519, 4663, 5113, 5167, 5419, 5437, 5653, 6301, 6427, 6661, 6679, 6967, 7723, 7741, 8011, 8389, 8713

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Prog

(PARI) forprime(p=2, 8800, x=0; while(x<p&&x^3%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(3^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(Magma) [p: p in PrimesUpTo(10000) | not exists{x: x in ResidueClassRing(p) | x^9 eq 2} and exists{x: x in ResidueClassRing(p) | x^3 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, 10^4, if (ok(p, 2, 3, 3^2), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A040028, A049596, A059262, A059667, A070179, A070181 - A070188.

Sequence in context: A031419 A183349 A238682 * A107198 A020354 A142846

Adjacent sequences: A070177 A070178 A070179 * A070181 A070182 A070183

Keyword

nonn,easy

Author

Klaus Brockhaus, Apr 29 2002

Status

approved