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Erdős problem 41

Let A ⊆ ℕ be an infinite set such that the triple sums a + b + c are all distinct for a, b, c in A (aside from the trivial coincidences). Is it true that liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0?

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Observation
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2415f78e850aeee50afdca525c6f2e0ea606f207
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