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A257302 Number of 4th power nonresidues modulo n.

%I A257302 #10 Apr 24 2015 18:29:22
%S A257302 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,
%T A257302 21,22,15,28,21,24,27,28,27,18,31,36,30,26,21,32,37,22,23,44,27,38,41,
%U A257302 44,39,34,43,48,37,42,29,52,45,30,47,58,57,42,33,58
%N A257302 Number of 4th power nonresidues modulo n.
%C A257302 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.
%H A257302 Stanislav Sykora, <a href="/A257302/b257302.txt">Table of n, a(n) for n = 1..10000</a>
%F A257302 a(n) = n - A052273(n).
%F A257302 Satisfies a(n) <= n-2 (residues 0 and 1 are always present).
%t A257302 Table[Length[Complement[Range[n - 1], Union[Mod[Range[n]^4, n]]]], {n, 100}] (* _Vincenzo Librandi_, Apr 20 2015 *)
%o A257302 (PARI) nrespowp(n,p) = {my(v=vector(n),d=0);
%o A257302   for(r=0,n-1,v[1+(r^p)%n]+=1);
%o A257302   for(k=1,n,if(v[k]==0,d++));
%o A257302   return(d);}
%o A257302 a(n) = nrespowp(n,4)
%Y A257302 Cf. A095972 (p=2), A257301 (p=3), A257303 (p=5).
%K A257302 nonn
%O A257302 1,4
%A A257302 _Stanislav Sykora_, Apr 19 2015