{"task": {"agent_timeout": 600, "task": "omnimath_69", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nAn integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition.\n[quote]For example, 4 can be partitioned in five distinct ways:\n4\n3 + 1\n2 + 2\n2 + 1 + 1\n1 + 1 + 1 + 1[/quote]\nThe number of partitions of n is given by the partition function $p\\left ( n \\right )$. So $p\\left ( 4 \\right ) = 5$ .\nDetermine all the positive integers so that $p\\left ( n \\right )+p\\left ( n+4 \\right )=p\\left ( n+2 \\right )+p\\left ( n+3 \\right )$.\n\n## Instructions\n\nSolve the mathematical problem above and write your final answer to `/workspace/answer.txt`.\n\n**Important**: Write only your final answer to the file, not the full solution process.\n\n### Guidelines\n\n- Provide your final numerical answer or mathematical expression\n- Write the answer as plain text (no special formatting needed)\n- Be precise and clear in your answer\n- The answer should directly respond to what the problem asks for\n\n### Example\n\nIf the problem asks \"What is 2 + 2?\", your answer file should contain:\n\n```\n4\n```\n\nYour answer will be evaluated against the correct solution using an automated grading system.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "math", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "omnimath", "tags": ["omni-math"]}, "runs": []}