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A257302 Number of 4th power nonresidues modulo n. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A118088 A088212 A085208 * A268715 A085211 A085212

Adjacent sequences:  A257299 A257300 A257301 * A257303 A257304 A257305

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Apr 19 2015

STATUS

approved

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Last modified June 27 17:44 EDT 2017. Contains 288790 sequences.