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A070188
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Primes p such that x^12 = 2 has a solution mod p, but x^(12^2) = 2 has no solution mod p.
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10
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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
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1,1
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LINKS
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PROG
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(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, ", ")));
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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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