On some Rado numbers for generalized arithmetic progressions
Abstract
The 2-color Rado number for the equation x1+x 2-2x3=c, which for each constant c∈Z we denote by S1(c), is the least integer, if it exists, such that every 2-coloring, Δ:[1,S1(c)]→{0,1}, of the natural numbers admits a monochromatic solution to x1+x2-2x3=c, and otherwise S1(c)=∞. We determine the 2-color Rado number for the equation x1+x2-2x3=c, when additional inequality restraints on the variables are added. In particular, the case where we require x2
Publication Title
Discrete Mathematics
Recommended Citation
Grynkiewicz, D. (2004). On some Rado numbers for generalized arithmetic progressions. Discrete Mathematics, 280 (1-3), 39-50. https://doi.org/10.1016/j.disc.2003.06.007
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