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

Author

Stanislav Sykora, Apr 19 2015

Keywords

• nonn

Comments

a(n) is the number of values r, 0<=r=0, (m^p)%n != r.

Links

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

Crossrefs

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

Programs

Mathematica

Table[Length[Complement[Range[n - 1], Union[Mod[Range[n]^5, n]]]], {n, 100}] (* Vincenzo Librandi, Apr 20 2015 *)

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)

Formula

a(n) = n-A052274(n).

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