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there are $\frac{n(n+1)}{2}$ distinct remainders

Source: Moldova TST 1997

August 8, 2023

Problem Statement

Find all integers n>1n>1 for which there exist positive integers a1,a2,…,ana_1,a_2,\ldots,a_n such that when divided by ai+aj,1≤i≤j≤na_i+a_j, 1\leq i\leq j\leq n there are n(n+1)2\frac{n(n+1)}{2} distinct remainders.
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