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A070180
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Primes p such that x^3 = 2 has a solution mod p, but x^(3^2) = 2 has no solution mod p.
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3
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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
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OFFSET
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1,1
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LINKS
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PROG
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(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, ", ")));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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