A192215 Number of zero trace primitive elements in Galois field GF(11^n).

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

Offset: 1

Author

Pasha Zusmanovich, Jun 25 2011

Keywords

• nonn
• hard
• more

Crossrefs

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

Programs

Sage

def a(n):
    ans = 0
    for x in GF(11^n):
        if x!=0 and x.trace()==0 and x.multiplicative_order()==11^n-1: ans += 1
    return ans  # Robin Visser, May 10 2024

Formula

a(n) = n * A192510(n). - Joerg Arndt, Jul 03 2011

Extensions

a(6)-a(7) from A192510 by Jean-François Alcover, Mar 02 2020

a(8)-a(10) from Robin Visser, May 10 2024