# omnimath / omnimath_1266 - 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 For any positive integers $a$ and $b$ with $b>1$, let $s_{b}(a)$ be the sum of the digits of $a$ when it is written in base $b$. Suppose $n$ is a positive integer such that $$\sum_{i=1}^{\left\lfloor\log _{23} n\right\rfloor} s_{20}\left(\left\lfloor\frac{n}{23^{i}}\right\rfloor\right)=103 \quad \text { and } \sum_{i=1}^{\left\lfloor\log _{20} n\right\rfloor} s_{23}\left(\left\lfloor\frac{n}{20^{i}}\right\rfloor\right)=115$$ Compute $s_{20}(n)-s_{23}(n)$. ## 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