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A070188 Primes p such that x^12 = 2 has a solution mod p, but x^(12^2) = 2 has no solution mod p. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
PROG
(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, ", ")));
/* Joerg Arndt, Sep 21 2012 */
CROSSREFS
Sequence in context: A142641 A070181 A001134 * A059331 A124586 A051110
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Apr 29 2002
STATUS
approved

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Last modified April 12 06:13 EDT 2024. Contains 371623 sequences. (Running on oeis4.)