2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77640In this paper we construct number fields ramified at 2 and 3 only, with various moderate-sized non-solvable Galois groups. We construct these fields by specializing three point covers, some from the literature and some new here. The specialization points come from solutions to a generalized Fermat equation. We conclude with a specific suggestion for further research and two general conjectures.Number Theorytext