A049580 Primes p such that x^48 = 2 has a solution mod p.

2, 23, 31, 47, 71, 89, 127, 167, 191, 223, 233, 239, 257, 263, 311, 359, 383, 431, 439, 479, 503, 599, 601, 647, 719, 727, 743, 839, 863, 881, 887, 911, 919, 983, 1031, 1103, 1151, 1223, 1289, 1319, 1327, 1367, 1399, 1423, 1433, 1439, 1471, 1487, 1511, 1559

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A212376 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Examples

			0^48 == 2 (mod 2). 8^48 == 2 (mod 23). 4^48 == 2 (mod 31). 7^48 == 2 (mod 47). 33^48 == 2 (mod 71). 5^48 == 2 (mod 89). 10^48 == 2 (mod 127). 49^48 == 2 (mod 167). 4^48 == 2 (mod 191). - _R. J. Mathar_, Jul 20 2025
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Index entries for related sequences

Crossrefs

Cf. A000040, A212376.

Programs

Magma

[p: p in PrimesUpTo(1600) | exists(t){x : x in ResidueClassRing(p) | x^48 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Mathematica

ok[p_]:= Reduce[Mod[x^48 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

PARI

N=10^4;  default(primelimit,N);
ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
forprime(p=2,N, if (ok(p,2,48),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */