On a Question Raised by Brown, Graham and Landman - Jungić, Veselin (Sarajevo Journal of Mathematics, 2024)
We construct non-periodic 2-colorings that avoid long mochromatic progressions having odd common differences. Also we prove that the set of all arithmetic progressions with common differences in $\left( \mathbb{N}!-1\right) \cup \mathbb{N}!\cup \left( \mathbb{N}!+1\right) - \{ 0\}$ does not have the $2$-Ramsey property. 2000 Mathematics Subject Classification. Primary 11B25; Secondary 05D10