Question 18
Given an integer $n \ge 2$, show that there exist $n+1$ pairwise distinct numbers $x_1, x_2, \dots, x_n, x_{n+1}$ in $\mathbb{Q} \setminus \mathbb{Z}$ such that $\{x_1^3\} + \{x_2^3\} + \dots + \{x_n^3\} = \{x_{n+1}^3\}$, where $\{x\}$ is the fractional part of the real number $x$.