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PAMO 2022 Problem 6 - Product is a power of 11

Source: 2022 Pan-African Mathematics Olympiad Problem 6

June 26, 2022
number theory

Problem Statement

Does there exist positive integers n1,n2,…,n2022n_1, n_2, \dots, n_{2022} such that the number (n12020+n22019)(n22020+n32019)⋯(n20212020+n20222019)(n20222020+n12019) \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 1111?
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