2024/09/04 by Pach, János, Zakharov, Dmitrii
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.03128
A subset S of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of elements of S are distinct. Imre Ruzsa asked the following question: What is the maximum number f(N) such that every set S of N real numbers contains a bi-Sidon subset of size at least f(N)? He proved that f(N)≥ cN\frac13, for a constant c>0. In this note, we improve this bound to N^\frac13+\frac778+o(1).