Question 68
Do there exist $2024$ non-zero reals $a_1, a_2, \dots, a_{2024}$, such that
$$
\sum_{i=1}^{2024} \left(a_i^2 + \frac{1}{a_i^2}\right) + 2 \sum_{i=1}^{2024} \frac{a_i}{a_{i+1}} + 2024 = 2 \sum_{i=1}^{2024} \left(a_i + \frac{1}{a_i}\right)?
$$
$$
\sum_{i=1}^{2024} \left(a_i^2 + \frac{1}{a_i^2}\right) + 2 \sum_{i=1}^{2024} \frac{a_i}{a_{i+1}} + 2024 = 2 \sum_{i=1}^{2024} \left(a_i + \frac{1}{a_i}\right)?
$$