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subsets of {-2^k, 2^k} fot k=0,1,...,2022

Source: 2022 Austrian Regional Competition For Advanced Students p4

October 4, 2022
combinatoricsnumber theory

Problem Statement

We are given the set M={−22022,−22021,...,−22,−2,−1,1,2,22,...,22021,22022}.M = \{-2^{2022}, -2^{2021}, . . . , -2^{2}, -2, -1, 1, 2, 2^2, . . . , 2^{2021}, 2^{2022}\}. Let TT be a subset of MM, such that neighbouring numbers have the same difference when the elements are ordered by size. (a) Determine the maximum number of elements that such a set TT can contain. (b) Determine all sets TT with the maximum number of elements.
(Walther Janous)
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