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Number of zero trace primitive elements in Galois field GF(11^n).
6

%I #22 May 10 2024 08:50:11

%S 0,0,48,320,5925,33936,691880,5107200,69610716,628484000

%N Number of zero trace primitive elements in Galois field GF(11^n).

%F a(n) = n * A192510(n). - _Joerg Arndt_, Jul 03 2011

%o (Sage)

%o def a(n):

%o ans = 0

%o for x in GF(11^n):

%o if x!=0 and x.trace()==0 and x.multiplicative_order()==11^n-1: ans += 1

%o return ans # _Robin Visser_, May 10 2024

%Y Cf. A192211, A192212, A192213, A192214, A192216 for other primes.

%K nonn,hard,more

%O 1,3

%A _Pasha Zusmanovich_, Jun 25 2011

%E a(6)-a(7) from A192510 by _Jean-François Alcover_, Mar 02 2020

%E a(8)-a(10) from _Robin Visser_, May 10 2024