Bounded Solutions to asigma(n) = bn + c¶
- Task ID:
math.sigma_linear_diophantine - Domain:
math - Subdomain:
number_theory - Status:
test - Tags:
number_theory,divisor_function,sigma_function,diophantine_equations,bounded_search,prime_sieve,search_tree,benchmark
Public Summary¶
This page is generated from task metadata and selected public-safe excerpts.
Example B1 Prompt Excerpt¶
You are working on a mathematical-computational research task in algorithmic number theory.
## Research goal
The generated input file `data/problem_instances.json` contains a bank of bounded instances for the equation
`a * sigma(n) = b * n + c`,
where `sigma(n)` is the sum-of-divisors function.
Each record gives an `instance_id` together with integers `a`, `b`, `c`, and `U`. For every instance, find all positive integers `n` with `1 <= n <= U` that satisfy the equation.
## Input data description
The JSON file contains a list of bounded search instances. Each instance has these fields:
Notes¶
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