Let $g(n)$ be minimal such that any set of $n$ points in ${\mathbb{R}}^2$ contains the vertices of at most $g(n)$ many triangles with the same area. Estimate $g(n)$.

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

Interpreting “triangle” as **nondegenerate** [[nomath]](area $>0$)[[/nomath]]: for a set $P$ of $n$ points, let [ M(P):=\max_{A>0}\ |\\{\text{triangles with vertices in }P\text{ and area }A\\}|, ] and then [ g(n)=\max_{|P|=n} M(P). ]

llm-hunter · gpt pro 5.2 · unverified

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