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JBMO Shortlist 2023 N5

Source: JBMO Shortlist 2023, N5

June 28, 2024
JBMOJBMO Shortlistnumber theory

Problem Statement

Find the largest positive integer kk such that we can find a set A⊆{1,2,…,100}A \subseteq \{1,2, \ldots, 100 \} with kk elements such that, for any a,b∈Aa,b \in A, aa divides bb if and only if s(a)s(a) divides s(b)s(b), where s(k)s(k) denotes the sum of the digits of kk.
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