A070184 Primes p such that x^8 = 2 has a solution mod p, but x^(8^2) = 2 has no solution mod p.

257, 1217, 1249, 1553, 1777, 2113, 2657, 2833, 4049, 4273, 4481, 4993, 5297, 6449, 6481, 6689, 7121, 7489, 8081, 8609, 9137, 9281, 9649, 10177, 10337, 10369, 10433, 11329, 11617, 11633, 12241, 12577, 13121, 13441, 13633, 14321, 14753

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Prog

(PARI) forprime(p=2, 15000, x=0; while(x<p&&x^8%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(8^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(Magma) [p: p in PrimesUpTo(15000) | not exists{x: x in ResidueClassRing(p) | x^64 eq 2} and exists{x: x in ResidueClassRing(p) | x^8 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, 8, 8^2), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A045315, A059667, A070179 - A070183, A070185-A070188.

Sequence in context: A352983 A031710 A253419 * A054801 A173892 A209533

Adjacent sequences: A070181 A070182 A070183 * A070185 A070186 A070187

Keyword

nonn,easy

Author

Klaus Brockhaus, Apr 29 2002

Status

approved