diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 3d12874..e5f4e2b 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1783,16 +1783,22 @@ def test_prod(self):
         self.assertRaises(TypeError, prod)
         self.assertRaises(TypeError, prod, 42)
         self.assertRaises(TypeError, prod, ['a', 'b', 'c'])
-        self.assertRaises(TypeError, prod, ['a', 'b', 'c'], '')
-        self.assertRaises(TypeError, prod, [b'a', b'c'], b'')
+        self.assertRaises(TypeError, prod, ['a', 'b', 'c'], start='')
+        self.assertRaises(TypeError, prod, [b'a', b'c'], start=b'')
         values = [bytearray(b'a'), bytearray(b'b')]
-        self.assertRaises(TypeError, prod, values, bytearray(b''))
+        self.assertRaises(TypeError, prod, values, start=bytearray(b''))
         self.assertRaises(TypeError, prod, [[1], [2], [3]])
         self.assertRaises(TypeError, prod, [{2:3}])
-        self.assertRaises(TypeError, prod, [{2:3}]*2, {2:3})
-        self.assertRaises(TypeError, prod, [[1], [2], [3]], [])
+        self.assertRaises(TypeError, prod, [{2:3}]*2, start={2:3})
+        self.assertRaises(TypeError, prod, [[1], [2], [3]], start=[])
+
+        # Some odd cases
+        self.assertEqual(prod([2, 3], start='ab'), 'abababababab')
+        self.assertEqual(prod([2, 3], start=[1, 2]), [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2])
+        self.assertEqual(prod([], start={2: 3}), {2:3})
+
         with self.assertRaises(TypeError):
-            prod([10, 20], [30, 40])     # start is a keyword-only argument
+            prod([10, 20], 1)     # start is a keyword-only argument
 
         self.assertEqual(prod([0, 1, 2, 3]), 0)
         self.assertEqual(prod([1, 0, 2, 3]), 0)
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index a2a2db2..16da008 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -3081,14 +3081,9 @@ math_prod_impl(PyObject *module, PyObject *iterable, PyObject *start)
     }
 
     if (result == NULL) {
-        result = PyLong_FromLong(1);
-        if (result == NULL) {
-            Py_DECREF(iter);
-            return NULL;
-        }
-    } else {
-        Py_INCREF(result);
+        result = _PyLong_GetOne();
     }
+    Py_INCREF(result);
 #ifndef SLOW_PROD
     /* Fast paths for integers keeping temporary products in C.
      * Assumes all inputs are the same type.
@@ -3104,7 +3099,7 @@ math_prod_impl(PyObject *module, PyObject *iterable, PyObject *start)
         }
         /* Loop over all the items in the iterable until we finish, we overflow
          * or we found a non integer element */
-        while(result == NULL) {
+        while (result == NULL) {
             item = PyIter_Next(iter);
             if (item == NULL) {
                 Py_DECREF(iter);