Question 114
Given a positive integer $n \gt 1$. An integer $a \gt n^2$ is chosen so that for each $i = 1, 2, \ldots, n$, the set $\{a + 1, a + 2, \ldots, a + n\}$ contains a multiple of the number $n^2 + i$. Prove that $a \gt n^4 - n^3$. (A. Golovanov)