Multiplicative Sidon sets in [1,n] exist with maximal gap ≪_ε n^{10/33 + ε}.
Stadlmann,On the mean square gap between primes, arXiv:2212.10867, 2022.https://arxiv.org/abs/ 2212.10867
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Gaps in Multiplicative Sidon Sets II
Multiplicative Sidon sets in [1,n] exist with maximal gap ≪_ε n^{10/33 + ε}.