MathNet 2024-part-04 — 168 problems (EN–VI) Question 118

Find all the integers $n$ such that there is a permutation $a_1, a_2, \dots, a_{1013}$ of the numbers $1012, 1013, \dots, 2024$, so that $a_1n^{1012} + a_2n^{1011} + \dots + a_{1012}n + a_{1013} = 0$.