A 2-coloring of [1,n] can have (n^2)/22 + O(n) monochromatic Schur triples, but not less!
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We prove that the minimum number (asymptotically) of monochromatic Schur triples that a 2-coloring of [1,n] can have is (n^2)/22 + O(n). This was solved independently by Tomasz Schoen.
4 pages, minor and subtle gap fixed, typos fixed
4 pages, minor and subtle gap fixed, typos fixed