A257302 Number of 4th power nonresidues modulo n.

0, 0, 1, 2, 3, 2, 3, 6, 5, 6, 5, 8, 9, 6, 11, 14, 12, 10, 9, 16, 13, 10, 11, 20, 19, 18, 17, 20, 21, 22, 15, 28, 21, 24, 27, 28, 27, 18, 31, 36, 30, 26, 21, 32, 37, 22, 23, 44, 27, 38, 41, 44, 39, 34, 43, 48, 37, 42, 29, 52, 45, 30, 47, 58, 57, 42, 33, 58

Offset

1,4

Comments

a(n) is the number of values r, 0<=r<n, such that, for p=4 and for any m>=0, (m^p)%n != r.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..10000

Formula

a(n) = n - A052273(n).

Satisfies a(n) <= n-2 (residues 0 and 1 are always present).

Mathematica

Table[Length[Complement[Range[n - 1], Union[Mod[Range[n]^4, n]]]], {n, 100}] (* Vincenzo Librandi, Apr 20 2015 *)

Prog

(PARI) nrespowp(n, p) = {my(v=vector(n), d=0);
  for(r=0, n-1, v[1+(r^p)%n]+=1);
  for(k=1, n, if(v[k]==0, d++));
  return(d); }
a(n) = nrespowp(n, 4)

Crossrefs

Cf. A095972 (p=2), A257301 (p=3), A257303 (p=5).

Sequence in context: A088212 A085208 A332553 * A268715 A085211 A085212

Adjacent sequences: A257299 A257300 A257301 * A257303 A257304 A257305

Keyword

nonn

Author

Stanislav Sykora, Apr 19 2015

Status

approved