An improved upper bound for the size of the multiplicative 3-Sidon sets

Original · EN

We say that a set is a multiplicative 3-Sidon set if the equation s₁s₂s₃=t₁t₂t₃ does not have a solution consisting of distinct elements taken from this set. In this paper we show that the size of a multiplicative 3-Sidon subset of {1,2,,n} is at most π(n)+π(n/2)+n²/³(n)²¹/³⁻¹/³⁺ᵒ⁽¹⁾, which improves the previously known best bound π(n)+π(n/2)+cn²/³ n/ n.