MathNet 2017-part-03 — 176 problems (EN–VI) Question 74

Decide if there is a permutation $a_1, a_2, \dots, a_{6666}$ of the numbers $1, 2, \dots, 6666$ with the property that the sum $k + a_k$ is a perfect square for all $k = 1, 2, \dots, 6666$.