Let $A$ be a finite set of integers. Is it true that for every $ϵ>0$$$\max (|A+A|,|AA|){\gg }_{ϵ}|A{|}^{2-ϵ}?$$

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

This is **open** in full generality. In fact, your inequality is essentially the **Erdős–Szemerédi sum–product conjecture** (for (h=2)), which asserts that for every (\epsilon>0), [ \max\bigl(|A+A|,\ |AA|\bigr)\ \ge c(\epsilon),|A|^{2-\epsilon} \qquad (A\subset\mathbb Z\ \text{finite}), ] equivalently (\max(|A+A|,|AA|)…

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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