Let $f (N)$ be the maximum size of $A \subseteq {1, \dots, N}$ 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 $f (N) \sim N^{1/3} ?$

Worked, still open.

additive combinatorics · open · prize $100 · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is the classic **(B_3)** (a.k.a. “Sidon of order 3”) extremal problem.

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

candidate solution ↗

oeis

A387704 — Size of the maximal subset S of {1,2,...,n} such that for all a, b, c in S not necessarily distinct, a+b+c is unique up to permutation.0,1,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

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Vela Sidon frontier (A309370) · verified work

A B₂/Sidon problem — the same object family as Vela's verified Sidon records, where nine improved terms were accepted into OEIS A309370 (the campaign's first external adoption).

OEIS A309370 ↗ · verified-combinatorics (witnesses + verify.py) ↗ · the Erdős campaign

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oeis

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