On the Blaschke conjecture for 3-webs

We 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 resolves the Blaschke conjecture for 3-webs. We also give the algorithm for determining whether a given 3-web is linearizable, find the linearity condition for 3-webs and establish its relationships to the condition that a plane curve consists of flexes and to the Euler equation in gas-dynamics.