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A192508
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Number of conjugacy classes of primitive elements in GF(5^n) which have trace 0.
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5
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0, 0, 4, 8, 54, 140, 1116, 2976, 19828, 58388, 443892
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OFFSET
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1,3
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COMMENTS
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Also number of primitive polynomials of degree n over GF(5) whose second-highest coefficient is 0.
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LINKS
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FORMULA
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PROG
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(GAP)
p := 5;
a := function(n)
local q, k, cnt, x;
q:=p^n; k:=GF(p, n); cnt:=0;
for x in k do
if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then
cnt := cnt+1;
fi;
od;
return cnt/n;
end;
for n in [1..16] do Print (a(n), ", "); od;
(Sage) # See A192507 (change first line p=3 to p=5)
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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