Question 132
Let $n \geq 1$. Find all permutations $(a_1, a_2, \ldots, a_n)$ of $(1,2, \ldots, n)$ for which
$$
\frac{a_k^2}{a_{k+1}} \leq k+2 \quad \text{for } k=1,2, \ldots, n-1
$$
$$
\frac{a_k^2}{a_{k+1}} \leq k+2 \quad \text{for } k=1,2, \ldots, n-1
$$