A257303 Number of 5th power nonresidues modulo n.

0, 0, 0, 1, 0, 0, 0, 3, 2, 0, 8, 3, 0, 0, 0, 7, 0, 4, 0, 5, 0, 16, 0, 9, 20, 0, 8, 7, 0, 0, 24, 15, 24, 0, 0, 15, 0, 0, 0, 15, 32, 0, 0, 35, 10, 0, 0, 21, 6, 40, 0, 13, 0, 16, 40, 21, 0, 0, 0, 15, 48, 48, 14, 30, 0, 48, 0, 17, 0, 0, 56, 37, 0, 0, 60, 19, 56, 0, 0, 35, 26, 64, 0, 21, 0, 0, 0, 73, 0

Offset

1,8

Comments

a(n) is the number of values r, 0<=r<n, such that, for p=5 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-A052274(n).

Satisfies a(n) <= n-3 (residues 0, 1, and n-1 are always present).

Mathematica

Table[Length[Complement[Range[n - 1], Union[Mod[Range[n]^5, 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, 5)

Crossrefs

Cf. A095972 (p=2), A257301 (p=3), A257302 (p=4).

Sequence in context: A067585 A173787 A116191 * A048199 A335998 A152441

Adjacent sequences: A257300 A257301 A257302 * A257304 A257305 A257306

Keyword

nonn

Author

Stanislav Sykora, Apr 19 2015

Status

approved