2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136804Any non-degenerate quadratic form over a Hilbertian field (e.g., a number field) is isomorphic to a scaled trace form. In this work we extend this result to more general fields. In particular, prosolvable and prime-to-p extensions of a Hilbertian field. The proofs are based on the theory of PAC extensions.10 pages; added results on prime-to-p extensions, removed the condition on the countability of the fieldsNumber Theorytext