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

Author

Don Reble, Sep 20 2001

Keywords

• nonn

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

Crossrefs

Cf. A040159.

Programs

PARI

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