Irreducible Polynomials over Finite Fields
WORLD SCIENTIFIC eBooks · 2011
For n = 1, 2, 3, . . .let N n (q) denote the number of monic irreducible polynomials over the finite field F q .We show that the sequence ( n N n (q)) n>e 3+7/(q-1) 2 is strictly increasing and the sequence ( n+1 N n+1 (q)/ n N n (q)) n 5.835×10 14 is strictly decreasing.We also prove that if q 9 then (N n+1 (q)/N n (q)) n 1 is strictly increasing.