Let $R(3;k)$ be the minimal $n$ such that if the edges of $K_n$ are coloured with $k$ colours then there must exist a monochromatic triangle. Determine$$\underset{k\to \infty }{\lim }R(3;k{)}^{1/k}.$$

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

Let $R(3;k)$ be the $k$-colour Ramsey number for triangles, i.e. the least $n$ such that every $k$-edge-colouring of (K_n) contains a monochromatic (K_3).

llm-hunter · gpt pro 5.2 · unverified

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