MathNet 2018-part-04 — 181 problems (EN–VI) Question 53

Determine the least real number $c$ satisfying the condition $\sum_{k=1}^{n} x_{k}^{2} \le cn$, for all positive integers $n$ and all real numbers $x_1, \dots, x_n$ greater than or equal to $-1$ such that $\sum_{k=1}^{n} x_{k}^{3} = 0$.