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A257303
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Number of 5th power nonresidues modulo n.
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3
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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
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OFFSET
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1,8
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COMMENTS
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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.
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LINKS
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FORMULA
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Satisfies a(n) <= n-3 (residues 0, 1, and n-1 are always present).
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MATHEMATICA
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Table[Length[Complement[Range[n - 1], Union[Mod[Range[n]^5, n]]]], {n, 100}] (* Vincenzo Librandi, Apr 20 2015 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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