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Number of zero trace primitive elements in Galois field GF(5^n).
6

%I #20 May 10 2024 08:50:08

%S 0,0,12,32,270,840,7812,23808,178452,583880,4882812,12434160,

%T 122070312,391954136,2630952180

%N Number of zero trace primitive elements in Galois field GF(5^n).

%F a(n) = n * A192508(n). - _Joerg Arndt_, Jul 03 2011

%o (Sage)

%o def a(n):

%o ans = 0

%o for x in GF(5^n):

%o if x!=0 and x.trace()==0 and x.multiplicative_order()==5^n-1: ans += 1

%o return ans # _Robin Visser_, May 10 2024

%Y Cf. A192508.

%Y Cf. A192211, A192212, A192214, A192215, A192216 for other primes.

%K nonn,hard,more

%O 1,3

%A _Pasha Zusmanovich_, Jun 25 2011

%E a(9)-a(11) from _Joerg Arndt_, Oct 03 2012

%E a(12)-a(15) from _Robin Visser_, May 10 2024