PAMO 2022 Problem 6

Day 2

Does there exist positive integers $n_1, n_2, \dots, n_{2022}$ such that the number $\left( n_1^{2020} + n_2^{2019} \right)\left( n_2^{2020} + n_3^{2019} \right) \cdots \left( n_{2021}^{2020} + n_{2022}^{2019} \right)\left( n_{2022}^{2020} + n_1^{2019} \right)$ is a power of $11$ ?

Dataset text AI-MO AoPS. Quoted with source.

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