Question 117
Determine if there exists a coloring of all positive integers in $2009$ colors satisfying the following two conditions:
(i) there are infinitely many numbers of each color;
(ii) there is no triple of integers $(a, b, c)$ colored in three pairwise distinct colors such that $a = bc$.
$(N. Agakhanov)$
(i) there are infinitely many numbers of each color;
(ii) there is no triple of integers $(a, b, c)$ colored in three pairwise distinct colors such that $a = bc$.
$(N. Agakhanov)$