# omnimath / omnimath_4173 - taskset: [omnimath](https://harnessreport.com/tasks/omnimath.md) - difficulty: hard - category: math - language: - runnable from the site: no - agent timeout: 600s ## Results by harness _none yet_ ## Instruction ``` # Mathematical Problem Two different integers $u$ and $v$ are written on a board. We perform a sequence of steps. At each step we do one of the following two operations: (i) If $a$ and $b$ are different integers on the board, then we can write $a + b$ on the board, if it is not already there. (ii) If $a$, $b$ and $c$ are three different integers on the board, and if an integer $x$ satisfies $ax^2 +bx+c = 0$, then we can write $x$ on the board, if it is not already there. Determine all pairs of starting numbers $(u, v)$ from which any integer can eventually be written on the board after a finite sequence of steps. ## Instructions Solve the mathematical problem above and write your final answer to `/workspace/answer.txt`. **Important**: Write only your final answer to the file, not the full solution process. ### Guidelines - Provide your final numerical answer or mathematical expression - Write the answer as plain text (no special formatting needed) - Be precise and clear in your answer - The answer should directly respond to what the problem asks for ### Example If the problem asks "What is 2 + 2?", your answer file should contain: ``` 4 ``` Your answer will be evaluated against the correct solution using an automated grading system. ``` --- 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