MathDB
Mean-free subset

Source: 2022 China TST, Test 1, P2 (posting for better LaTeX)

March 24, 2022
combinatoricsnumber theoryprime numbers

Problem Statement

Let pp be a prime, AA is an infinite set of integers. Prove that there is a subset BB of AA with 2pāˆ’22p-2 elements, such that the arithmetic mean of any pairwise distinct pp elements in BB does not belong to AA.
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