Myers's conjecture on a three-color Rado number

From papers

Let R3(E)R_3(\mathcal{E}) denote the smallest nn such that every 3-coloring of [n][n] induces a monochromatic solution to the equation E\mathcal{E}. For m3m\ge 3, consider the equation xy=(m2)zx-y=(m-2)z. Myers's conjecture.

R3(xy=(m2)z)=m3m2m1.R_3(x-y=(m-2)z)=m^3-m^2-m-1.

This conjecture gives exact values for a family of generalized Schur-related Rado numbers. The source does not state whether it has been resolved.

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Sources & referencesView supporting material

Primary source

Yuan Chang, Jesús A. De Loera and William J. Wesley, “Rado Numbers and SAT Computations”, arXiv:2210.03262 (2022).

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