A040119 Primes p such that x^4 = 10 has a solution mod p.

2, 3, 5, 31, 37, 41, 43, 53, 67, 71, 79, 83, 107, 151, 163, 173, 191, 199, 227, 239, 241, 271, 277, 283, 307, 311, 317, 347, 359, 397, 431, 439, 443, 467, 479, 523, 547, 563, 587, 599, 613, 631, 641, 643, 683, 719

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A040121 (complement in the primes).

Programs

Magma

[p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 10}]; // Vincenzo Librandi, Sep 12 2012

Mathematica

ok [p_]:=Reduce[Mod[x^4 - 10, p]== 0, x, Integers]=!= False; Select[Prime[Range[180]], ok] (* Vincenzo Librandi, Sep 12 2012 *)

PARI

isA040119(p)={r=0;for(m=0,p-1,if(Mod(m,p)^4==Mod(10,p),r=1));r} \\ Michael B. Porter, Oct 13 2009

PARI

select( {is_A040119(p)=ispower(Mod(10, p), 4)}, primes(199)) \\ is_A040119(p) assumes that p is prime, else append "&& isprime(p)". - M. F. Hasler, Nov 19 2024

Extensions

Definition corrected by Michael B. Porter, Oct 13 2009