A059899 Primes p such that x^3 = 2 has more than one solution mod p and the sum of the (three) solutions is p.

31, 229, 397, 439, 457, 499, 601, 643, 691, 727, 739, 811, 919, 997, 1021, 1051, 1093, 1327, 1459, 1657, 1699, 1753, 1933, 1999, 2113, 2179, 2203, 2251, 2281, 2341, 2347, 2383, 2671, 2731, 2767, 2791, 2833, 2953, 2971, 3061, 3229, 3259, 3331, 3373, 3391

Offset: 1

Author

Klaus Brockhaus, Mar 02 2001

Keywords

• nonn

Comments

Subsequence of A040028 and of A014752, complement of A059914 relative to A014752. Solutions mod p are represented by integers from 0 to p-1.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A040028, A014752, A059914.

Programs

Maple

filter:= proc(p) local S;
  if not isprime(p) then return false fi;
  S:= map(t -> rhs(t[1]), [msolve(x^3=2,p)]);
  nops(S) = 3 and convert(S,`+`) = p
end proc:
select(filter, [seq(i,i=7..5000, 6)]); # Robert Israel, Aug 13 2024