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

Author

Klaus Brockhaus, Apr 29 2002

Keywords

• nonn
• easy

Crossrefs

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

Programs

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

forprime(p=2,4250,x=0; while(x
				

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 */