Abstract
We give a construction of a set \(A \subset \mathbb N\) such that any subset \({A' \subset A}\) with \(|A'| \gg |A|^{2/3}\) is neither an additive nor multiplicative Sidon set. In doing so, we refute a conjecture of Klurman and Pohoata.
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Acknowledgements
We are very grateful to Cosmin Pohoata for bringing this problem to our attention, and for several helpful discussions. Thanks also to Ben Green, Oleksiy Klurman, Sarah Peluse, Ilya Shkredov and Sophie Stevens for helpful discussions.
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The authors were supported by the Austrian Science Fund FWF Projects P 30405-N32 and P 34180.
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Roche-Newton, O., Warren, A. Additive and multiplicative Sidon sets. Acta Math. Hungar. 165, 326–336 (2021). https://doi.org/10.1007/s10474-021-01160-8
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DOI: https://doi.org/10.1007/s10474-021-01160-8