2019/08/30 by Thotsaporn "Aek'' Thanatipanonda, Thanatipanonda, Thotsaporn "Aek''
Mathematics · #Algebraic and Geometric Analysis #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.CO
paper · pdf · doi:10.48550/arxiv.1908.11516
10 pages
arxiv created 2019/08/30 · openalex publication_date 2019/08/30 · arxiv updated 2019/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Rado numbers of the regular equations E(b) of the form c1x1+c2x2+…+ ck-1xk-1 = xk + b, where b ∈ ℤ and ci ∈ ℤ+ for all i. We give the upper bounds and the sufficient condition for the lower bounds for t-color Rado numbers r(E(b);t) in terms of r(E(0);t) for both b>0 and b<0. We also give examples where the exact values of Rado numbers are obtained from these results.