Two-color Rado number of x plus y plus c =<i> kz</i> for large c

초록

For positive integers c and k, we consider the equation L : x + y + c = kz. Two-color Rado number R = R(c, k) of L is the least integer, provided that it exists, such that every two-coloring of 1, 2, & BULL; & BULL; & BULL;, R admits a monochromatic solution to L. The Rado number R(c, k) exists if and only if k is odd or c is even. In this paper, we show that ifk is odd or c is even with k & GE; 5 and c & GE; 2k3 + 2k2 - k, then & UGamma;2 c +2  k +c the two-color Rado number of L is equal to N = , as predicted by Jones and k Schaal.& COPY; 2023 Elsevier B.V. All rights reserved.

키워드