Erdős Problem #863

What the AI did

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 $r\ge 2$.

Verification

Marked solved by erdosproblems.com's official status. Solve credited via Terence Tao's AI-contributions wiki.

Source

• Problem recorderdosproblems.com