BALKAN-SL 2011 C3
Is it possible to partition the set of positive integer numbers into two classes, none of which contains an infinite arithmetic sequence (with a positive ratio)? What is we impose the extra condition that in each class of the partition, the set of difference \begin{align*} \left{ \min { n \in \mathcal{C} \mid n >m } -m \mid m \in \mathcal{C} \right } \end{align*} be bounded?
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