Thotsaporn ThanatipanondaElaine WongMahidol University2018-12-212019-03-142018-12-212019-03-142017-05-05Electronic Journal of Combinatorics. Vol.24, No.2 (2017)107789262-s2.0-85019119627https://repository.li.mahidol.ac.th/handle/20.500.14594/42384© 2017, Australian National University. All rights reserved. The solution to the problem of finding the minimum number of monochromatic triples (x, y, x + ay) with a ≥ 2 being a fixed positive integer over any 2-coloring of [1, n] was conjectured by Butler, Costello, and Graham (2010) and Thanathipanonda (2009). We solve this problem using a method based on Datskovsky’s proof (2003) on the minimum number of monochromatic Schur triples (x, y, x + y). We do this by exploiting the combinatorial nature of the original proof and adapting it to the general problem.Mahidol UniversityComputer ScienceArticleSCOPUS