A070181 Primes p such that x^4 = 2 has a solution mod p, but x^(4^2) = 2 has no solution mod p.

113, 281, 353, 577, 593, 617, 1033, 1049, 1097, 1153, 1193, 1201, 1217, 1249, 1481, 1553, 1601, 1753, 1777, 1889, 2129, 2273, 2281, 2393, 2473, 2689, 2833, 2857, 3049, 3089, 3121, 3137, 3217, 3313, 3361, 3529, 3673, 3761, 3833, 4001, 4049, 4153, 4217

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Prog

(PARI) forprime(p=2, 4250, x=0; while(x<p&&x^4%p!=2%p, x++); if(x<p, y=0; while(y<p&&y^(4^2)%p!=2%p, y++); if(y==p, print1(p, ", "))))
(Magma) [p: p in PrimesUpTo(5000) | not exists{x: x in ResidueClassRing(p) | x^16 eq 2} and exists{x: x in ResidueClassRing(p) | x^4 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, 4, 4^2), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A040098, A045315, A045316, A059667, A070179, A070180, A070182 - A070188.

Sequence in context: A142947 A325067 A142641 * A001134 A070188 A059331

Adjacent sequences: A070178 A070179 A070180 * A070182 A070183 A070184

Keyword

nonn,easy

Author

Klaus Brockhaus, Apr 29 2002

Status

approved