Question 91
Let $n$ be an integer not less than $3$ and let $a_1, a_2, \dots, a_n$ be a finite sequence of positive integers, such that, for $k = 2, 3, \dots, n$
$$
n(a_k + 1) - (n-1)a_{k-1} = 1.
$$
Prove that $a_n$ is not divisible by $(n-1)^2$.
$$
n(a_k + 1) - (n-1)a_{k-1} = 1.
$$
Prove that $a_n$ is not divisible by $(n-1)^2$.