2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120486Let q be a prime power and N_n count degree-n monic irreducible polynomials in F_q[x]. We show that prod_{n=1}^{\infty} (1 -z^n)^N_n = 1 - qz for small |z|.2 pages. v.1 replaced because the proof of absolute convergence was valid only on reals. (It used l'Hopital.) Sadder news: "...you've simply rediscovered the Weil conjectures for P^1. ..." (email from Kevin Buzzard)Number Theory11T99text