Problem detail · source-aware
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If Sidon sets $A, B \subseteq \{1, \dots, N\}$ satisfy $(A-A) \cap (B-B) = \{0\}$, must $\binom{|A|}{2} + \binom{|B|}{2} \le \binom{f(N)}{2} + O(1)$, where $f(N)$ is the largest Sidon-set size in $[N]$ - and can the bound be improved by a fixed proportion when $|A| = |B|$?
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The equal-size bound is disproved by an explicit construction; the unrestricted bound fails as a consequence of the resolution of Erdős Problem #42.
Provider: OpenAI / Harmonic / Anthropic · Prompt public: unknown · Independence: unknown
The official Erdős problems record marks both questions answered negatively, with component Lean proofs.
Correctness: unknown · statement fidelity: unaudited · peer review: none
both proposed bounds fail
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.