2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68542We settle an old question about the existence of certain "sums-of-squares" formulas over a field F (which are the simplest examples of composition formulas for quadratic forms). A classical theorem says that if such a formula exists over a field of characteristic 0, then certain binomial coefficients must be even. We use motivic cohomology to prove that the same result holds in characteristic p.Rings and AlgebrasAlgebraic GeometryAlgebraic Topologytext