# sympy__sympy-18199
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on my analysis of the issue and the existing patch example, I can generate the proper patch. The issue is that `nthroot_mod` doesn't check for the case where `a % p == 0`, which means `x = 0` should be a valid root.

```
--- a/sympy/ntheory/residue_ntheory.py
+++ b/sympy/ntheory/residue_ntheory.py
@@ -746,6 +746,14 @@ def nthroot_mod(a, n, p, all_roots=False):
     a, n, p = as_int(a), as_int(n), as_int(p)
     if n < 1:
         raise ValueError("n should be positive")
+
+    # If a % p == 0, then x = 0 is a root since 0**n = 0 = a mod p
+    if a % p == 0:
+        if all_roots:
+            return [0]
+        else:
+            return 0
+
     if a % p == 1:
         if all_roots:
             return [1]
```