The Ramsey number of the clique and the hypercube

The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of the edges of the complete graph KN on N vertices contains either a red n-dimensional hypercube, or a blue clique on s vertices. Answering a question of Burr and Erdős from 1983, and improving on recent results of Conlon, Fox, Lee and Sudakov, and of the current authors, we show that r(Ks,Qn)=(s−1)(2n−1)+1 for every s∈N and every sufficiently large n∈N.