2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99152We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and sufficient for a 3-web to be linearizable. This solves the Blaschke conjecture for 3-webs. As a side result, we show that the number of linearizations in the Gronwall conjecture does not exceed fifteen and give criteria for rigidity of 3-webs.LaTeX, 52 pagesDifferential Geometry53A60text