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A070183
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Primes p such that x^6 = 2 has a solution mod p, but x^(6^2) = 2 has no solution mod p.
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3
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17, 41, 137, 401, 433, 449, 457, 521, 569, 641, 761, 809, 857, 919, 929, 953, 977, 1361, 1409, 1423, 1657, 1697, 1999, 2017, 2081, 2143, 2153, 2287, 2297, 2417, 2609, 2633, 2729, 2753, 2777, 2791, 2801, 2897, 2953, 3041, 3209, 3329, 3457, 3593, 3617
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OFFSET
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1,1
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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MAPLE
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select(p -> isprime(p) and [msolve(x^6=2, p)]<>[] and [msolve(x^36=2, p)]=[] , [seq(i, i=3..10^4, 2)]); # Robert Israel, May 13 2018
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PROG
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(PARI) forprime(p=2, 3700, x=0; while(x<p&&x^6%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(6^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(Magma) [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^36 eq 2} and exists{x: x in ResidueClassRing(p) | x^6 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, 6, 6^2), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */
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CROSSREFS
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Cf. A040992, A049568, A059264, A059667, A070179 - A070182, A070184 - A070188.
Sequence in context: A139961 A188661 A205171 * A201705 A165668 A269425
Adjacent sequences: A070180 A070181 A070182 * A070184 A070185 A070186
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KEYWORD
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nonn,easy
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AUTHOR
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Klaus Brockhaus, Apr 29 2002
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STATUS
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approved
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