diff --git a/Data/Mod.hs b/Data/Mod.hs
--- a/Data/Mod.hs
+++ b/Data/Mod.hs
@@ -352,8 +352,10 @@
   :: Natural -- Value
   -> Natural -- Modulo
   -> Maybe Natural
+invertModInternal 0 1 = Just 0
 invertModInternal x m = case integerRecipMod# (toInteger x) m of
-  (# | () #) -> Nothing
+  -- See https://gitlab.haskell.org/ghc/ghc/-/issues/26017
+  (# | () #) -> if m == 1 then Just 0 else Nothing
   (# y | #)  -> Just y
 {-# INLINABLE invertModInternal #-}
 
@@ -383,11 +385,10 @@
 #endif
 {-# INLINABLE [1] (^%) #-}
 
-{-# SPECIALISE [1] (^%) ::
-  KnownNat m => Mod m -> Integer -> Mod m,
-  KnownNat m => Mod m -> Natural -> Mod m,
-  KnownNat m => Mod m -> Int     -> Mod m,
-  KnownNat m => Mod m -> Word    -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Integer -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Natural -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Int     -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Word    -> Mod m #-}
 
 {-# RULES
 "powMod/2/Integer"     forall x. x ^% (2 :: Integer) = let u = x in u*u
diff --git a/Data/Mod/Compat.hs b/Data/Mod/Compat.hs
--- a/Data/Mod/Compat.hs
+++ b/Data/Mod/Compat.hs
@@ -14,9 +14,14 @@
   , remWord2#
   ) where
 
-#ifdef aarch64_HOST_ARCH
-import GHC.Exts (Word(..), Word#, timesWord#)
+#if defined(aarch64_HOST_ARCH) && __GLASGOW_HASKELL__ < 912
 
+import GHC.Exts (Word(..), Word#)
+
+#if __GLASGOW_HASKELL__ < 904
+
+import GHC.Exts (timesWord#)
+
 timesWord2# :: Word# -> Word# -> (# Word#, Word# #)
 timesWord2# x y = (# z, timesWord# x y #)
   where
@@ -24,6 +29,12 @@
 {-# INLINE timesWord2# #-}
 
 foreign import capi unsafe "aarch64.h umulh" c_umulh :: Word -> Word -> Word
+
+#else
+
+import GHC.Exts (timesWord2#)
+
+#endif
 
 remWord2# :: Word# -> Word# -> Word# -> Word#
 remWord2# lo hi m = r
diff --git a/Data/Mod/Word.hs b/Data/Mod/Word.hs
--- a/Data/Mod/Word.hs
+++ b/Data/Mod/Word.hs
@@ -335,6 +335,8 @@
 invertMod mx@(Mod !x) = case natVal mx of
   NatJ#{}   -> tooLargeModulus
   NatS# 0## -> Nothing
+  -- See https://gitlab.haskell.org/ghc/ghc/-/issues/26017
+  NatS# 1## -> Just 0
   NatS# m#  -> Mod <$> invertModWord x (W# m#)
 
 invertModWord :: Word -> Word -> Maybe Word
@@ -442,11 +444,10 @@
       f b  e acc = f (mulMod m b b) (e `P.quot` 2) (if odd e then mulMod m b acc else acc)
 {-# INLINABLE [1] (^%) #-}
 
-{-# SPECIALISE [1] (^%) ::
-  KnownNat m => Mod m -> Integer -> Mod m,
-  KnownNat m => Mod m -> Natural -> Mod m,
-  KnownNat m => Mod m -> Int     -> Mod m,
-  KnownNat m => Mod m -> Word    -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Integer -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Natural -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Int     -> Mod m #-}
+{-# SPECIALISE [1] (^%) :: KnownNat m => Mod m -> Word    -> Mod m #-}
 
 {-# RULES
 "powMod/2/Integer"     forall x. x ^% (2 :: Integer) = let u = x in u*u
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,7 @@
+# 0.2.1.0
+
+* Fix `invertMod (0 :: Mod 1)`.
+
 # 0.2.0.1
 
 * Fix build on `aarch64`.
diff --git a/mod.cabal b/mod.cabal
--- a/mod.cabal
+++ b/mod.cabal
@@ -1,5 +1,5 @@
 name:          mod
-version:       0.2.0.1
+version:       0.2.1.0
 cabal-version: >=1.10
 build-type:    Simple
 license:       MIT
@@ -15,7 +15,7 @@
   Originally part of the <https://hackage.haskell.org/package/arithmoi arithmoi> package.
 category:      Math, Number Theory
 author:        Andrew Lelechenko <andrew.lelechenko@gmail.com>
-tested-with:   GHC ==9.0.2 GHC ==9.2.5 GHC ==9.4.4 GHC ==9.6.1
+tested-with:   GHC ==9.0.2 GHC ==9.2.8 GHC ==9.4.8 GHC ==9.6.7 GHC ==9.8.4 GHC ==9.10.2 GHC ==9.12.2 GHC ==9.14.1
 extra-source-files:
   changelog.md
   README.md
@@ -36,15 +36,15 @@
 library
   build-depends:
     base >=4.15 && <5,
-    deepseq,
-    ghc-bignum
+    deepseq <1.6,
+    ghc-bignum <1.5
   if flag(semirings)
     build-depends:
-      semirings >= 0.5
+      semirings >=0.5 && <0.8
   if flag(vector)
     build-depends:
-      primitive,
-      vector >= 0.12
+      primitive <0.10,
+      vector >=0.12 && <0.14
   exposed-modules:
     Data.Mod
     Data.Mod.Word
@@ -53,7 +53,7 @@
   default-language: Haskell2010
   ghc-options: -Wall -O2 -Wno-deprecations -Wcompat
 
-  if(arch(aarch64))
+  if(arch(aarch64) && impl(ghc <9.12))
     c-sources: cbits/aarch64.c
     include-dirs: cbits
 
@@ -63,7 +63,7 @@
     mod,
     quickcheck-classes-base,
     tasty >=0.10,
-    tasty-quickcheck >=0.9 && <0.11
+    tasty-quickcheck >=0.9 && <0.12
   if flag(semirings)
     build-depends:
       containers,
diff --git a/test/Test.hs b/test/Test.hs
--- a/test/Test.hs
+++ b/test/Test.hs
@@ -58,6 +58,8 @@
   [ testGroup "Mod 1" $
     testProperty "fromInteger"
       (fromIntegerProp (Proxy :: Proxy 1)) :
+    testProperty "invertMod"
+      (invertMod (0 :: Mod 1) == Just 0) :
     map lawsToTest (laws1 (Proxy :: Proxy (Mod 1)))
   , testMod(2310)
   , testMod(2^16-1)
@@ -103,6 +105,8 @@
   , testGroup "Word.Mod 1" $
     testProperty "fromInteger"
       (fromIntegerWordProp (Proxy :: Proxy 1)) :
+    testProperty "invertMod"
+      (Word.invertMod (0 :: Word.Mod 1) == Just 0) :
     map lawsToTest (laws1 (Proxy :: Proxy (Word.Mod 1)))
   , testMod(2310)
   , testMod(2^16-1)