diff --git a/loopy/type_inference.py b/loopy/type_inference.py
index 258717472..f1d17230a 100644
--- a/loopy/type_inference.py
+++ b/loopy/type_inference.py
@@ -429,6 +429,47 @@ def map_quotient(self, expr: p.Quotient):
         else:
             return self.combine([n_dtype_set, d_dtype_set])
 
+    def _map_int_div_modulo(self, expr: p.FloorDiv | p.Remainder):
+        n_dtype_set = self.rec(expr.numerator)
+        d_dtype_set = self.rec(expr.denominator)
+
+        if not (n_dtype_set and d_dtype_set):
+            return cast("list[NumpyType]", [])
+
+        n_dtype = cast("NumpyType", n_dtype_set[0]).dtype
+        d_dtype = cast("NumpyType", d_dtype_set[0]).dtype
+        num = (
+            np.empty(0, dtype=n_dtype)
+            if not is_integer(expr.numerator)
+            else expr.numerator
+        )
+        denom = (
+            np.empty(0, dtype=d_dtype)
+            if not is_integer(expr.denominator)
+            else expr.denominator
+        )
+        denom = (
+            cast("int | np.integer", denom + 1)
+            if is_integer(denom) and denom == 0
+            else denom
+        )  # avoid divide by zero.
+
+        if is_integer(num) and is_integer(denom):
+            return self.rec(num // denom)
+
+        floor_div_np = num // denom
+        assert isinstance(floor_div_np, np.ndarray)
+
+        return [NumpyType(floor_div_np.dtype)]
+
+    @override
+    def map_floor_div(self, expr: p.FloorDiv):
+        return self._map_int_div_modulo(expr)
+
+    @override
+    def map_remainder(self, expr: p.Remainder):
+        return self._map_int_div_modulo(expr)
+
     @override
     def map_constant(self, expr: object):
         if isinstance(expr, np.generic):
diff --git a/test/test_loopy.py b/test/test_loopy.py
index 8badf6016..2f3995d55 100644
--- a/test/test_loopy.py
+++ b/test/test_loopy.py
@@ -3733,6 +3733,20 @@ def test_type_cast_parse_stringify_roundtrip():
     assert expr == parsed
 
 
+def test_floor_div_modulo_with_uint_index():
+    # See <https://github.com/inducer/loopy/issues/999>
+    knl = lp.make_kernel(
+        "{[i]: 0<=i<10}",
+        "a[map[i] // 2, map[i] % 35] = i",
+        [
+            lp.GlobalArg("map", dtype=np.uint64, shape=lp.auto),
+            lp.GlobalArg("a", dtype=np.float64, shape=(10, 4)),
+        ],
+    )
+    # check the codegen is successful
+    lp.generate_code_v2(knl).device_code()
+
+
 if __name__ == "__main__":
     import sys
     if len(sys.argv) > 1: