Publication at Faculty of Mathematics and Physics |
2010
Abstract
In this paper we introduce a Ramsey type function S(r; a, b, c) as the maximum s such that for any r-coloring of N there is a monochromatic sequence x1, x2, . . . , xs satisfying a homogeneous second order linear recurrence ax{i} + bx{i+1} + cx{i+2} = 0, 1 <= i <= s − 2. We investigate S(2; a, b, c) and evaluate its values for a wide class of triples (a, b, c).