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Bounded Solutions to a*sigma(n) = b*n + c

  • Task ID: math.sigma_linear_diophantine
  • Domain: math
  • Subdomain: number_theory
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: number_theory, divisor_function, sigma_function, diophantine_equations, bounded_integer_problems, arithmetic_functions

Runtime and requirements

  • Estimated time: 10-60 minutes
  • Python: >=3.11
  • Packages: None
  • GPU required: no
  • Network required: no

Public input and output contract

Inputs

  • problem_instances.json (data): Generated bounded instances with fields instance_id, split, a, b, c, and U.

Outputs

  • analysis.py (code): Agent-written solver that defines solve(a, b, c, U) or find_solutions(a, b, c, U).
  • results/solutions.csv (data): All solutions as rows (instance_id, n), one row per valid n.
  • results/instance_summary.csv (data): Per-instance summary with solution_count and largest_solution.

Public repository files

View this task in ASI-Bench

Formal benchmark task directories in the public repository are metadata-only. Versioned prompts and inputs are distributed through the pinned benchmark dataset.

Provenance

This task is included in the current seed42 benchmark set at dataset revision f11a199f71fb4b854ac43a1bf548d5df519141a9.

This page is generated only from files tracked in the public ASI-Bench repository at commit f18382f03faf. Submission bundles, run logs, private scoring configuration, and private reference answers are not read by this page generator.