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A257303 Number of 5th power nonresidues modulo n. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A152441 A248181

Adjacent sequences:  A257300 A257301 A257302 * A257304 A257305 A257306

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Apr 19 2015

STATUS

approved

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Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.