diff --git a/Lib/test/test_math_integer_aug.py b/Lib/test/test_math_integer_aug.py
new file mode 100644
index 00000000000..2b3593b7f5a
--- /dev/null
+++ b/Lib/test/test_math_integer_aug.py
@@ -0,0 +1,125 @@
+import math
+import sys
+import unittest
+
+import math.integer as intmath
+
+
+class IndexLike:
+
+    def __init__(self, value):
+        self.value = value
+
+    def __index__(self):
+        return self.value
+
+
+class BadIndex:
+
+    def __index__(self):
+        raise RuntimeError('bad index')
+
+
+def py_factorial(n):
+    result = 1
+    for value in range(2, n + 1):
+        result *= value
+    return result
+
+
+def py_perm(n, k=None):
+    if k is None:
+        k = n
+    if k > n:
+        return 0
+    result = 1
+    for value in range(n - k + 1, n + 1):
+        result *= value
+    return result
+
+
+def py_comb(n, k):
+    if k > n:
+        return 0
+    k = min(k, n - k)
+    if k < 0:
+        return 0
+    numerator = denominator = 1
+    for value in range(1, k + 1):
+        numerator *= n - k + value
+        denominator *= value
+    return numerator // denominator
+
+
+class IntegerSubmoduleAugmentedTests(unittest.TestCase):
+
+    def test_module_identity_and_alias_metadata(self):
+        self.assertIs(math.integer, intmath)
+        self.assertIs(sys.modules['math.integer'], intmath)
+        self.assertEqual(intmath.__name__, 'math.integer')
+        for name in ('comb', 'factorial', 'gcd', 'isqrt', 'lcm', 'perm'):
+            with self.subTest(name=name):
+                self.assertIs(getattr(math, name), getattr(intmath, name))
+                self.assertEqual(getattr(intmath, name).__module__, 'math.integer')
+
+    def test_gcd_lcm_variadic_and_index_edges(self):
+        self.assertEqual(intmath.gcd(), 0)
+        self.assertEqual(intmath.gcd(-6), 6)
+        self.assertEqual(intmath.gcd(6, 10, 15), 1)
+        self.assertEqual(intmath.gcd(1, IndexLike(99), IndexLike(101)), 1)
+        with self.assertRaises(RuntimeError):
+            intmath.gcd(1, BadIndex())
+
+        self.assertEqual(intmath.lcm(), 1)
+        self.assertEqual(intmath.lcm(-6), 6)
+        self.assertEqual(intmath.lcm(0, IndexLike(5), IndexLike(7)), 0)
+        self.assertEqual(intmath.lcm(21, 6, 14), 42)
+        with self.assertRaises(RuntimeError):
+            intmath.lcm(0, BadIndex())
+
+    def test_isqrt_factorial_boundary_paths(self):
+        for value in (0, 1, 2, 15, 16, 2**63 - 1, 2**64, (1 << 200) + 12345):
+            with self.subTest(value=value):
+                root = intmath.isqrt(IndexLike(value))
+                self.assertLessEqual(root * root, value)
+                self.assertLess(value, (root + 1) * (root + 1))
+        with self.assertRaises(ValueError):
+            intmath.isqrt(IndexLike(-1))
+        with self.assertRaises(RuntimeError):
+            intmath.isqrt(BadIndex())
+
+        for value in (0, 1, 5, 20, 25, 80, 130, 300):
+            with self.subTest(value=value):
+                self.assertEqual(intmath.factorial(IndexLike(value)), py_factorial(value))
+        with self.assertRaises(ValueError):
+            intmath.factorial(-1)
+        with self.assertRaises(RuntimeError):
+            intmath.factorial(BadIndex())
+
+    def test_perm_comb_small_large_and_error_paths(self):
+        perm_cases = [
+            (5, None), (3, 5), (5, 2), (200, 3), (30, 22),
+            (2**70, 2), (2**70 + 9, 3),
+        ]
+        for n, k in perm_cases:
+            with self.subTest(kind='perm', n=n, k=k):
+                args = (IndexLike(n),) if k is None else (IndexLike(n), IndexLike(k))
+                self.assertEqual(intmath.perm(*args), py_perm(n, k))
+        with self.assertRaises(ValueError):
+            intmath.perm(5, -1)
+        with self.assertRaises(RuntimeError):
+            intmath.perm(IndexLike(5), BadIndex())
+
+        comb_cases = [
+            (3, 5), (5, 2), (200, 3), (80, 40),
+            (2**70, 2), (2**70 + 9, 3),
+        ]
+        for n, k in comb_cases:
+            with self.subTest(kind='comb', n=n, k=k):
+                self.assertEqual(intmath.comb(IndexLike(n), IndexLike(k)), py_comb(n, k))
+        with self.assertRaises(ValueError):
+            intmath.comb(5, -1)
+        with self.assertRaises(OverflowError):
+            intmath.comb(2**70, 2**69)
+        with self.assertRaises(RuntimeError):
+            intmath.comb(IndexLike(5), BadIndex())
diff --git a/Lib/test/test_math_integer_p2p_aug.py b/Lib/test/test_math_integer_p2p_aug.py
new file mode 100644
index 00000000000..9927bb13c55
--- /dev/null
+++ b/Lib/test/test_math_integer_p2p_aug.py
@@ -0,0 +1,21 @@
+import statistics
+import unittest
+from fractions import Fraction
+
+
+class NumericBackwardsCompatibilityAugmentedTests(unittest.TestCase):
+
+    def test_fraction_and_statistics_unmodified(self):
+        value = Fraction(355, 113)
+        self.assertEqual(value.limit_denominator(100), Fraction(311, 99))
+        self.assertTrue(Fraction(12, 4).is_integer())
+        data = [Fraction(1, 3), Fraction(2, 3), Fraction(4, 3)]
+        self.assertEqual(statistics.mean(data), Fraction(7, 9))
+        self.assertEqual(statistics.median(data), Fraction(2, 3))
+
+    def test_complex_arithmetic_unmodified(self):
+        z = complex(3, 4)
+        self.assertEqual(z.conjugate(), complex(3, -4))
+        self.assertEqual(z * complex(0, 1), complex(-4, 3))
+        with self.assertRaises(ZeroDivisionError):
+            z / 0