MathNet 2024-part-02 — 168 problems (EN–VI) Question 166

Let $N \ge 3$ be an integer, and $a_0, \dots, a_{N-1}$ be pairwise distinct reals so that $a_i \ge a_{2i}$ for all $i$ (indices are taken mod $N$). Find all possible $N$ for which this is possible.