Let $a_1, a_2, ..., a_{n-1}$ be $n - 1$ consecutive positive integers in increasing order such that $k$ ${n \choose k}$ $\equiv 0$ (mod $a_k$), for all $k \in \{1, 2, ... , n - 1\}$. Find the possible values of $a_1$.
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Tags: number theory, Combinations, 6th edition
Let $a_1, a_2, ..., a_{n-1}$ be $n - 1$ consecutive positive integers in increasing order such that $k$ ${n \choose k}$ $\equiv 0$ (mod $a_k$), for all $k \in \{1, 2, ... , n - 1\}$. Find the possible values of $a_1$.