Problem

Source: 2024 CWMO P2

Tags: Sequence, algebra



Find all integers $k$, such that there exists an integer sequence ${\{a_n\}}$ satisfies two conditions below (1) For all positive integers $n$,$a_{n+1}={a_n}^3+ka_n+1$ (2) $|a_n| \leq M$ holds for some real $M$