Question 71
Find all positive integers $n$ and sequences of integers $a_0, a_1, \dots, a_n$ such that $a_n \neq 0$ and
$$
f(a_{i-1}) = a_i
$$
for all $i = 1, 2, \dots, n$, where $f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$.
$$
f(a_{i-1}) = a_i
$$
for all $i = 1, 2, \dots, n$, where $f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$.