--- /dev/null
+++ b/Mathlib/Unsorry/SumThreeSquaresZmodSixteenNeFifteen.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_three_squares_zmod_sixteen_ne_fifteen (a b c : ℤ) : (((a ^ 2 + b ^ 2 + c ^ 2 : ℤ)) : ZMod 16) ≠ 15 := by
+  first
+    | (push_cast; generalize (a : ZMod 16) = z0; generalize (b : ZMod 16) = z1; generalize (c : ZMod 16) = z2; revert z0 z1 z2; decide)
+    | (generalize (a : ZMod 16) = z0; generalize (b : ZMod 16) = z1; generalize (c : ZMod 16) = z2; revert z0 z1 z2; decide)
+    | (push_cast; decide)
+    | decide