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A070180 Primes p such that x^3 = 2 has a solution mod p, but x^(3^2) = 2 has no solution mod p. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)