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%I #38 Oct 18 2014 10:06:05
%S 0,0,3,4,15,12,63,72,207,290,979,864,4095,5250,13485,16496,65535,
%T 69948,262143,240000,888888,1319758,4106167,3318144,16199225,22355866,
%U 56730861,66385676,266917769,267331800,1073741823,1073809184,3481794591,5726404746,16262257795
%N Number of zero trace primitive elements in Galois field GF(2^n).
%D R. Lidl and H. Niederreiter, Finite Fields, 2nd ed., Cambridge Univ. Press, 1997. Chapter 2 discusses primitivity in sections 1-2 and trace in section 3.
%H W.-S. Chou and S.D. Cohen, <a href="http://dx.doi.org/10.1006/ffta.2000.0284">Primitive elements with zero traces</a>, Finite Fields and Their Appl. 7 (2001), 125-141; DOI:10.1006/ffta.2000.0284.
%F a(n) = n * A152049(n). [_Joerg Arndt_, Jul 03 2011]
%o (GAP)
%o p := 2;
%o for n in [1..17] do
%o F := GF(p^n);
%o num := 0;
%o for f in F do
%o if (f = Zero(F)) then continue; fi;
%o if (Trace(f) <> Zero(F)) then continue; fi;
%o if (Order(f) <> Size(F) - 1) then continue; fi;
%o num := num + 1;
%o od;
%o Print (num, ",");
%o od;
%Y Cf. A192212, A192213, A192214, A192215, A192216 for other primes.
%Y Cf. A152049, A107222.
%K nonn,hard
%O 1,3
%A _Pasha Zusmanovich_, Jun 25 2011
%E Terms 69948, ..., 1073809184 from _Joerg Arndt_, Jun 26 2011
%E Terms >1073809184 from _Joerg Arndt_, Jul 03 2011
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