--- /dev/null
+++ b/Mathlib/Unsorry/SexticX6PlusX3PlusOneCompositeShift.lean
@@ -0,0 +1,9 @@
+/-
+Copyright (c) 2026 Chris Barlow. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Chris Barlow
+-/
+import Mathlib.Tactic.Ring
+
+theorem sextic_x6_plus_x3_plus_one_dvd_pow_nine_sub_one (n : ℤ) : (n ^ 6 + n ^ 3 + 1) ∣ (n ^ 9 - 1) :=
+  ⟨n ^ 3 - 1, by ring⟩