Show that for $k\ge 3$$$\mathrm{ex}(n;C_{2k})\gg n^{1+\frac{1}{k}}.$$

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

The inequality [ \mathrm{ex}(n;C_{2k})\gg n^{1+\frac1k}\qquad (k\ge 3) ] is **not known in general**: it is a famous open problem of Erdős (sometimes called the *even cycle problem*). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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