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http://dx.doi.org/10.11568/kjm.2020.28.2.379

2-COLOR RADO NUMBER FOR x1 + x2 + ⋯ + xn = y1 + y2 = z  

Kim, Byeong Moon (Department of Mathematics Gangneung-Wonju National University)
Hwang, Woonjae (Division of Applied Mathematical Sciences Korea University)
Song, Byung Chul (Department of Mathematics Gangneung-Wonju National University)
Publication Information
Korean Journal of Mathematics / v.28, no.2, 2020 , pp. 379-389 More about this Journal
Abstract
An r-color Rado number N = R(𝓛, r) for a system 𝓛 of equations is the least integer, provided it exists, such that for every r-coloring of the set {1, 2, …, N}, there is a monochromatic solution to 𝓛. In this paper, we study the 2-color Rado number R(𝓔, 2) for 𝓔 : x1 + x2 + ⋯ + xn = y1 + y2 = z when n ≥ 4.
Keywords
Rado number; Schur number; Ramsey theory; r-coloring;
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