--- /dev/null
+++ b/Mathlib/Unsorry/SumTwoSquaresZmodEightNeSix.lean
@@ -0,0 +1,13 @@
+/-
+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
+
+theorem sum_two_squares_zmod_eight_ne_six (m n : ℤ) : (((m ^ 2 + n ^ 2 : ℤ)) : ZMod 8) ≠ 6 := by
+  first
+    | (push_cast; generalize (m : ZMod 8) = z0; generalize (n : ZMod 8) = z1; revert z0 z1; decide)
+    | (generalize (m : ZMod 8) = z0; generalize (n : ZMod 8) = z1; revert z0 z1; decide)
+    | (push_cast; decide)
+    | decide