In a first (theoretical) part of this paper, we prove a number of constraints on hypothetical counterexamples to the Casas-Alvero conjecture, building on ideas of Graf von Bothmer, Labs, Schicho and van de Woestijne that were recently reinterpreted by Draisma and de Jong in terms of p-adic valuations. In a second (computational) part, we present ideas improving upon Diaz-Toca and Gonzalez-Vega’...
