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JBMO TST 2020 - Moldova P12

Source: JBMO TST 2020 Moldova

October 13, 2020
combinatoricscombinatorics unsolvedunsolved

Problem Statement

Find all numbers n∈N∗n \in \mathbb{N}^* for which there exists a finite set of natural numbers A=(a1,a2,...an)A=(a_1, a_2,...a_n) so that for any kk (1≤k≤n)(1\leq k \leq n) the number aka_k is the number of all multiples of kk in set AA.
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