ycb_sympy_pr18199

what a new run launched now would send

nthroot_mod function misses one root of x = 0 mod p.
When in the equation x**n = a mod p , when a % p == 0. Then x = 0 mod p is also a root of this equation. But right now `nthroot_mod` does not check for this condition. `nthroot_mod(17*17, 5 , 17)` has a root `0 mod 17`. But it does not return it.

Work only inside this repository checkout. Make the code change the task
describes, keeping the diff focused — no drive-by refactors.

When you are done, leave your changes committed or in the working tree;
they are collected automatically.

Stay on this snapshot checkout (`task/ycb_sympy_pr18199`). Never checkout, pull, or rebase onto `main`. That branch is a README-only orphan.
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Some past runs of this task were launched with a different prompt (the prompt template changed since, or those runs predate this benchmark's stored prompt). Each run persists the exact prompt it sent at launch — that per-launch record is the audit trail; this page shows only the current one.