OPENHARDnumber theorySidon setsadditive combinatorics
Let $A\subset\mathbb{N}$ be an infinite set such that the triple sums $a+b+c$ are all distinct (aside from trivial coincidences). Is it true that $\liminf |A\cap \{1,\ldots,N\}|/N^{1/3}=0$?
Notes: Nash proved the result for h=4. Chen proved it for all even h. The problem remains open for odd h >= 3.
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