Problem 241

Erdős Problem #241: declared status 'open'. Formalized: yes. Let $f(N)$ be the maximum size of $A\subseteq \{1,\ldots,N\}$ such that the sums $a+b+c$ with $a,b,c\in A$ are all distinct (aside from the trivial coincidences). Is it true that$$f(N)\sim N^{1/3}?$$ Current best: Bose and Chowla [BoCh62] provided a construction proving one half of this, namely$$(1+o(1))N^{1/3}\leq f(N).$$The best upper bound known to date is due to Green [Gr01],$$f(N) \leq ((7/2)^{1/3}+o(1))N^{1/3}$$(note that $(7/2)^{1/3}\approx 1.519$). Prize: $100. OEIS: A387704. Tags: additive combinatorics, sidon sets.