A059858 Primes p such that x^5 == 2 (mod p) has five solutions.

151, 241, 251, 431, 571, 641, 911, 971, 1181, 1811, 2011, 2351, 2381, 2411, 2731, 3061, 3121, 3221, 3251, 3301, 3331, 3361, 3391, 3541, 3761, 3821, 3881, 4211, 4751, 4861, 4871, 4931, 5021, 5381, 5441, 5471, 5581, 5641, 5711, 5821, 5861

Offset

1,1

Comments

For any prime modulus, there must be exactly 0, 1 or 5 solutions to the equation with x between 0 and p - 1.

Primes == 1 (mod 5) such that 2 is a quintic residue, that is, primes p such that 2^((p-1)/5) == 1 (mod p). - Jianing Song, Jan 27 2019

Links

Table of n, a(n) for n=1..41.

Prog

(PARI) forstep(p=11, 5000, 10, if(isprime(p)&&Mod(2, p)^((p-1)/5)==1, print1(p, ", "))) \\ Jianing Song, Jan 27 2019

Crossrefs

Cf. A040159.

Sequence in context: A142225 A334769 A334931 * A152310 A276264 A070182

Adjacent sequences: A059855 A059856 A059857 * A059859 A059860 A059861

Keyword

nonn

Author

Don Reble, Sep 20 2001

Status

approved