2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121948Let $F_q$ be a finite field of characteristic $p=2,3$. We give the number of irreducible polynomials $x^m+a_{m-1}x^{m-1}+...+a_0\in\F_q[x]$ with $a_{m-1}$ and $a_{m-3}$ prescribed for any given $m$ if $p=2$, and with $a_{m-1}$ and $a_1$ prescribed for $m=1,...,10$ if $p=2,3$.17 pages, Part of the results was presented at the Polynomials over Finite Fields and Applications workshop at Banff International Research Station, CanadaNumber TheoryCombinatorics11T06; 05A15text