A070182 Primes p such that x^5 = 2 has a solution mod p, but x^(5^2) = 2 has no solution mod p.

151, 251, 3251, 3301, 4751, 8501, 11251, 11701, 13751, 14251, 14951, 15551, 16451, 17401, 18401, 21401, 21601, 24251, 28351, 28901, 32251, 32401, 32801, 34301, 36151, 36451, 37201, 40351, 42451, 42701, 44201, 45751, 46051, 46451, 46901

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Prog

(PARI) forprime(p=2, 47000, x=0; while(x<p&&x^5%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(5^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(Magma) [p: p in PrimesUpTo(50000) | not exists{x: x in ResidueClassRing(p) | x^25 eq 2} and exists{x: x in ResidueClassRing(p) | x^5 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, 5, 5^2), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A040159, A049557, A059313, A059667, A070179 - A070181, A070183 - A070188.

Sequence in context: A059858 A152310 A276264 * A100200 A142575 A142657

Adjacent sequences: A070179 A070180 A070181 * A070183 A070184 A070185

Keyword

nonn,easy

Author

Klaus Brockhaus, Apr 29 2002

Status

approved