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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 (N!-1) N! (N!+1) - \ 0\ does not have the 2-Ramsey property. 2000 Mathematics Subject Classification. Primary 11B25; Secondary 05D10
Veselin Jungić (Wed,) studied this question.