# ineqmath / 18 - taskset: [ineqmath](https://harnessreport.com/tasks/ineqmath.md) - difficulty: difficult - category: math reasoning - language: - runnable from the site: no - agent timeout: 3600s ## Results by harness _none yet_ ## Instruction ``` Solve the following problem. Reason step by step, create the file /app/answer.txt, and put your final answer there. Task description: Please solve the problem with clear, rigorous, and logically sound steps. At the end of your response, state your answer in exactly this format: 'The answer is $C=X$', where X is your calculated numerical bound value. Example: 'The answer is $C=1$'. Problem: Let $a, b, c, m, n$ be positive real numbers. Find the largest constant $C$ such that the following inequality holds for all $a, b, c, m, n \in \mathbb{R}^{+}$: $$ \frac{a^2}{b(m a+n b)}+\frac{b^2}{c(m b+n c)}+\frac{c^2}{a(m c+n a)} \geq \frac{C}{m+n}. $$ Solution: ``` --- Harness Report runs agent harnesses from their GitHub repos on Harbor tasks and records every model call. Every page is also `.md` and `.json`; index: https://harnessreport.com/llms.txt · MCP: https://harnessreport.com/mcp