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There exist a bounded set of positive real numbers S

Source: 7th European Mathematical Cup , Senior Category , Q3

December 25, 2018
algebraemcmath olympiad

Problem Statement

For which real numbers k>1k > 1 does there exist a bounded set of positive real numbers SS with at least 33 elements such that k(a−b)∈Sk(a - b)\in S for all a,b∈Sa,b\in S with a>b?a > b? Remark: A set of positive real numbers SS is bounded if there exists a positive real number MM such that x<Mx < M for all x∈S.x \in S.
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