diff --git a/cyclotomic.cabal b/cyclotomic.cabal
--- a/cyclotomic.cabal
+++ b/cyclotomic.cabal
@@ -1,5 +1,5 @@
 Name:                cyclotomic
-Version:             1.0.1
+Version:             1.1.0
 Stability:           stable
 Synopsis:            A subfield of the complex numbers for exact calculation.
 Description:         The cyclotomic numbers are a subset of the
@@ -17,7 +17,7 @@
 License-file:        LICENSE
 Author:              Scott N. Walck
 Maintainer:          Scott N. Walck <walck@lvc.edu>
-Copyright:           (c) Scott N. Walck 2012-2019
+Copyright:           (c) Scott N. Walck 2012-2020
 Category:            Math
 Build-type:          Simple
 Extra-source-files:  test/Properties.hs
@@ -39,7 +39,7 @@
   Exposed-modules:   Data.Complex.Cyclotomic, Data.Number.RealCyclotomic
   Build-depends:     base >= 4.2 && < 4.14,
                      containers >= 0.3,
-                     arithmoi >= 0.5
+                     arithmoi >= 0.9
   default-language:  Haskell2010
   Hs-source-dirs:    src
 
diff --git a/src/Data/Complex/Cyclotomic.hs b/src/Data/Complex/Cyclotomic.hs
--- a/src/Data/Complex/Cyclotomic.hs
+++ b/src/Data/Complex/Cyclotomic.hs
@@ -1,7 +1,7 @@
 {-# OPTIONS_GHC -Wall #-}
 {-# LANGUAGE Trustworthy #-}
 
-{- | 
+{- |
 Module      :  Data.Complex.Cyclotomic
 Copyright   :  (c) Scott N. Walck 2012-2017
 License     :  GPL-3 (see LICENSE)
@@ -10,23 +10,23 @@
 
 The cyclotomic numbers are a subset of the complex numbers with
 the following properties:
-    
+
      1.  The cyclotomic numbers are represented exactly, enabling exact
      computations and equality comparisons.
-    
+
      2.  The cyclotomic numbers contain the Gaussian rationals
      (complex numbers of the form 'p' + 'q' 'i' with 'p' and 'q' rational).
      As a consequence, the cyclotomic numbers are a dense subset of the
      complex numbers.
-    
+
      3.  The cyclotomic numbers contain the square roots of all rational numbers.
-    
+
      4.  The cyclotomic numbers form a field:  they are closed under addition, subtraction,
      multiplication, and division.
-    
+
      5.  The cyclotomic numbers contain the sine and cosine of all rational
      multiples of pi.
-    
+
      6.  The cyclotomic numbers can be thought of as the rational field extended
      with 'n'th roots of unity for arbitrarily large integers 'n'.
 
@@ -121,9 +121,16 @@
     , findWithDefault
     , fromListWith
     )
-import Math.NumberTheory.Primes.Factorisation
-    ( factorise
+import Math.NumberTheory.ArithmeticFunctions
+    ( runFunction
+    , totientA
+    , smallOmegaA
+    , isNFreeA
     )
+import Math.NumberTheory.Primes
+    ( unPrime
+    , factorise
+    )
 
 -- | A cyclotomic number.
 data Cyclotomic = Cyclotomic { order  :: Integer
@@ -223,8 +230,8 @@
 sqrtPositiveInteger n
     | n < 1      = error "sqrtPositiveInteger needs a positive integer"
     | otherwise  = let factors = factorise n
-                       factor = product [p^(m `div` 2) | (p,m) <- factors]
-                       nn     = product [p^(m `mod` 2) | (p,m) <- factors]
+                       factor = product [unPrime p ^ (m `div` 2) | (p, m) <- factors]
+                       nn     = product [unPrime p ^ (m `mod` 2) | (p, m) <- factors]
                    in case nn `mod` 4 of
                         1 -> fromInteger factor * (2 * eb nn + 1)
                         2 -> fromInteger factor * sqrt2 * sqrtPositiveInteger (nn `div` 2)
@@ -344,14 +351,8 @@
       (phi,nrp,sqfree) = phiNrpSqfree (order c)
 
 -- | Compute phi(n), the number of prime factors, and test if n is square-free.
---   We do these all together for efficiency, so we only call factorise once.
-phiNrpSqfree :: Integer -> (Integer,Int,Bool)
-phiNrpSqfree n = (phi,nrp,sqfree)
-    where
-      factors = factorise n
-      phi = foldr (\p n' -> n' `div` p * (p-1)) n [p | (p,_) <- factors]
-      nrp = length factors
-      sqfree = all (<=1) [m | (_,m) <- factors]
+phiNrpSqfree :: Integer -> (Integer, Int, Bool)
+phiNrpSqfree = runFunction $ (,,) <$> totientA <*> smallOmegaA <*> isNFreeA 2
 
 equalCoefficients :: Cyclotomic -> Maybe Rational
 equalCoefficients (Cyclotomic _ mp)
@@ -369,7 +370,7 @@
 tryReduce c
     = foldr reduceByPrime c squareFreeOddFactors
       where
-        squareFreeOddFactors = [p | (p,m) <- factorise (order c), p > 2, m <= 1]
+        squareFreeOddFactors = [unPrime p | (p, m) <- factorise (order c), unPrime p > 2, m <= 1]
 
 reduceByPrime :: Integer -> Cyclotomic -> Cyclotomic
 reduceByPrime p c@(Cyclotomic n _)
@@ -401,12 +402,12 @@
 removeExps n p q = concatMap (includeMods n q) $ map ((n `div` q) *) [-m..m]
     where m = (q `div` p - 1) `div` 2
 
-pqPairs :: Integer -> [(Integer,Integer)]
-pqPairs n = map (\(p,k) -> (p,p^k)) (factorise n)
+pqPairs :: Integer -> [(Integer, Integer)]
+pqPairs n = map (\(p, k) -> (unPrime p, unPrime p ^ k)) (factorise n)
 
 extraneousPowers :: Integer -> [(Integer,Integer)]
 extraneousPowers n
-    | n < 1      = error "extraneousPowers needs a postive integer"
+    | n < 1      = error "extraneousPowers needs a positive integer"
     | otherwise  = nub $ concat [[(p,r) | r <- removeExps n p q] | (p,q) <- pqPairs n]
 
 -- | Sum of two cyclotomic numbers.