Problem detail · source-aware
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Ho and GPT-5.4 Pro observed that a positive answer follows by connecting existing results: a routine adaptation of the Erdős-Turán bound for Sidon sets, together with a construction of Cilleruelo, Ruzsa, and Trujillo, gives $c'_r < c_r$ for all $r\ge 2$.
Provider: unknown · Prompt public: unknown · Independence: unknown
Marked solved by erdosproblems.com's official status. Solve credited via Terence Tao's AI-contributions wiki.
Correctness: unknown · statement fidelity: unaudited · peer review: none
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Source-reported tools: argument.
Independent: unknown · difference confidence: 0
The source did not supply a mathematical statement; retrieve it before replay or verification. VibeMath has not independently audited the mathematical statement, proof, or novelty claim.