23 lines
1022 B
Diff
23 lines
1022 B
Diff
Based on the GitHub issue about `nthroot_mod` function in sympy, I understand the problem:
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When solving `x**n = a mod p`, if `a % p == 0`, then `x = 0 mod p` is a valid root. The current implementation doesn't check for this case. The example given is `nthroot_mod(17*17, 5, 17)` which should return `0` as a root since `17*17 % 17 == 0` and `0**5 % 17 == 0`.
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Based on my knowledge of the sympy codebase and the `nthroot_mod` function in `sympy/ntheory/residue_ntheory.py`, here's the patch to fix this issue:
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--- a/sympy/ntheory/residue_ntheory.py
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+++ b/sympy/ntheory/residue_ntheory.py
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@@ -746,6 +746,14 @@ def nthroot_mod(a, n, p, all_roots=False):
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from sympy.core.numbers import igcdex
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a, n, p = as_int(a), as_int(n), as_int(p)
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a = a % p
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+
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+ # Handle the case when a % p == 0
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+ if a == 0:
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+ if all_roots:
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+ return [0]
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+ else:
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+ return 0
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+
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if n == 2:
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return sqrt_mod(a, p, all_roots)
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# see Hackman "Elementary Number Theory" (2009), page 76
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