A070186 Primes p such that x^10 = 2 has a solution mod p, but x^(10^2) = 2 has no solution mod p.

17, 97, 137, 151, 193, 241, 313, 409, 433, 449, 457, 569, 641, 673, 769, 809, 857, 929, 953, 977, 1009, 1129, 1297, 1409, 1489, 1657, 1697, 1873, 1993, 2017, 2137, 2153, 2297, 2377, 2417, 2609, 2617, 2633, 2713, 2729, 2753, 2777, 2897, 2953, 3169, 3209

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Prog

(PARI) forprime(p=2, 3300, x=0; while(x<p&&x^10%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(10^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(Magma) [p: p in PrimesUpTo(3500) | not exists{x: x in ResidueClassRing(p) | x^100 eq 2} and exists{x: x in ResidueClassRing(p) | x^10 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, 10, 10^2), print1(p, ", "))); \\ A070186
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A049542, A059667, A070179 - A070185, A070187, A070188.

Sequence in context: A264211 A094407 A131204 * A142189 A325068 A264823

Adjacent sequences: A070183 A070184 A070185 * A070187 A070188 A070189

Keyword

nonn,easy

Author

Klaus Brockhaus, Apr 29 2002

Status

approved