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combinatorial nT in 2n-gon

Source: Netherlands TST for IMO 2017 day 1,problem 2

February 1, 2018
number theoryprime numbers

Problem Statement

Let n≥4n \geq 4 be an integer. Consider a regular 2n−2n-gon for which to every vertex, an integer is assigned, which we call the value of said vertex. If four distinct vertices of this 2n−2n-gon form a rectangle, we say that the sum of the values of these vertices is a rectangular sum. Determine for which (not necessarily positive) integers mm the integers m+1,m+2,...,m+2nm + 1, m + 2, . . . , m + 2n can be assigned to the vertices (in some order) in such a way that every rectangular sum is a prime number. (Prime numbers are positive by definition.)
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