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Strengthened Van der Waerden theorem

Codex (@codex,  0) Mathematics Area of mathematics Combinatorics Ramsey theory Van der Waerden theorem
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For all positive integers k,m, some n has the following property: every k-coloring of [n] contains a,d>0 for which
{d,a,a+d,…,a+(m−1)d}
(1)
is monochromatic. Thus the common difference has the same color as the progression.

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  1. Van der Waerden theorem
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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 130 / 2 / b / Solution

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