Problem

Source: Serbia TST 2018 P6

Tags: algebra, combinatorics



For any positive integer $n$, define $$c_n=\min_{(z_1,z_2,...,z_n)\in\{-1,1\}^n} |z_1\cdot 1^{2018} + z_2\cdot 2^{2018} + ... + z_n\cdot n^{2018}|.$$Is the sequence $(c_n)_{n\in\mathbb{Z}^+}$ bounded?