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least no to be deleted such that sum of any 2 in {1,2,...,2n-1,2n}is composite

Source: 1998 Belarus TST 7.1

December 25, 2020
number theorycompositioncombinatorics

Problem Statement

Let n≥2n\ge 2 be positive integer. Find the least possible number of elements of tile set A={1,2,...,2n−1,2n}A =\{1,2,...,2n-1,2n\} that should be deleted in order to the sum of any two different elements remained be a composite number.
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