The number of monochromatic Schur triples
Solving a problem of Graham, Rödl and Ruciński, it is shown that in every 2-coloring of the set \(\{1,\ldots,N\}\) one can find at least \(N^2/22 + O(N)\) monochromatic Schur triples, i.e.~monochromatic solutions of the equation \(x+y=z\). Moreover, based on this result the exact value of the infimum number of Schur triples in any 2-coloring of \(\{1,\ldots,N\}\) can be found.
scientific article; zbMATH DE number 1417662