A192213 Number of zero trace primitive elements in Galois field GF(5^n).

0, 0, 12, 32, 270, 840, 7812, 23808, 178452, 583880, 4882812, 12434160, 122070312, 391954136, 2630952180

Offset: 1

Author

Pasha Zusmanovich, Jun 25 2011

Keywords

• nonn
• hard
• more

Crossrefs

Cf. A192508.

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

Programs

Sage

def a(n):
    ans = 0
    for x in GF(5^n):
        if x!=0 and x.trace()==0 and x.multiplicative_order()==5^n-1: ans += 1
    return ans  # Robin Visser, May 10 2024

Formula

a(n) = n * A192508(n). - Joerg Arndt, Jul 03 2011

Extensions

a(9)-a(11) from Joerg Arndt, Oct 03 2012

a(12)-a(15) from Robin Visser, May 10 2024