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Romania TST 2016 Day 3 P3

Source: Romania TST 2016 Day 3 P3

November 1, 2017
combinatorics

Problem Statement

Given a positive integer nn, show that for no set of integers modulo nn, whose size exceeds 1+n+41+\sqrt{n+4}, is it possible that the pairwise sums of unordered pairs be all distinct.
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