CONO-SUR 2021 Problem 5

Given an integer $n \geq 3$ , determine if there are $n$ integers $b_1, b_2, \dots , b_n$ , distinct two-by-two (that is, $b_i \neq b_j$ for all $i \neq j$ ) and a polynomial $P(x)$ with coefficients integers, such that $P(b_1) = b_2, P(b_2) = b_3, \dots , P(b_{n-1}) = b_n$ and $P(b_n) = b_1$ .