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if x∈A then 2x∉A, maximize |A|

Source: France 1991 P4

May 14, 2021
Setsnumber theory

Problem Statement

Let pp be a nonnegative integer and let n=2pn=2^p. Consider all subsets AA of the set {1,2,…,n}\{1,2,\ldots,n\} with the property that, whenever x∈Ax\in A, 2x∉A2x\notin A. Find the maximum number of elements that such a set AA can have.
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