Problem

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Tags: number theory



Let $n$ be a positive integer and $M = {1, 2, . . . , 2n + 1}$. Find out in how many ways we can split the set $M$ into three mutually disjoint nonempty sets $A,B,C$ so that both the following are true: (i) for each $a \in A$ and $b \in B$, the remainder of the division of $a$ by $b$ belongs to $C$ (ii) for each $c \in C$ there exists $a \in A$ and $b \in B$ such that $c$ is the remainder of the division of $a$ by $b$.