diff --git a/arithmetic.cabal b/arithmetic.cabal
--- a/arithmetic.cabal
+++ b/arithmetic.cabal
@@ -1,5 +1,5 @@
 name: arithmetic
-version: 1.4
+version: 1.5
 category: Number Theory
 synopsis: Natural number arithmetic
 license: MIT
@@ -14,7 +14,7 @@
   Lucas sequences, the Williams p+1 factorization method, continued fraction
   representations of natural number square roots, the Jacobi symbol, the
   Tonelli-Shanks algorithm for finding square roots modulo a prime, and
-  the Chakravala method for solving Pell's equation.
+  the Chakravala method for solving the Pell equation.
 
 Library
   build-depends:
diff --git a/src/Arithmetic/Pell.hs b/src/Arithmetic/Pell.hs
--- a/src/Arithmetic/Pell.hs
+++ b/src/Arithmetic/Pell.hs
@@ -1,6 +1,6 @@
 {- |
 module: Arithmetic.Pell
-description: Pell's equation (a^2 = n*b^2 + 1)
+description: The Pell equation a^2 = n*b^2 + 1
 license: MIT
 
 maintainer: Joe Leslie-Hurd <joe@gilith.com>
@@ -18,7 +18,7 @@
 
 -------------------------------------------------------------------------------
 -- Using the Chakravala method to find the fundamental solution of
--- Pell's equation
+-- the Pell equation
 --
 --   a^2 = n*b^2 + 1
 --
@@ -39,7 +39,7 @@
         b' = (a + b * m) `div` k
         j = case Modular.divide k (Modular.negate k a) b of
               Just i -> i
-              Nothing -> error "pell: couldn't divide"
+              Nothing -> error "Pell.chakravala: couldn't divide"
         m = minM j k
 
     sqrtN = Quadratic.rootFloor n
@@ -51,7 +51,7 @@
         m_1 = m_0 + k
 
 -------------------------------------------------------------------------------
--- Finding all integer solutions of Pell's equation
+-- Finding all integer solutions of the Pell equation
 -------------------------------------------------------------------------------
 
 solutions :: Natural -> [(Natural,Natural)]
@@ -68,4 +68,4 @@
 solution n =
     case solutions n of
       _ : ab : _ -> ab
-      _ -> error "Pell's equation a^2 = n*b^2 + 1 has no nontrivial integer solution when n is square"
+      _ -> error "The Pell equation a^2 = n*b^2 + 1 has no nontrivial integer solution when n is square"
diff --git a/src/Test.hs b/src/Test.hs
--- a/src/Test.hs
+++ b/src/Test.hs
@@ -512,21 +512,12 @@
     p = Polynomial.fromCoefficients r (map (Ring.fromNatural r) ps)
     q = Polynomial.fromCoefficients r (map (Ring.fromNatural r) (qs ++ [1]))
 
-propPellEquation :: Natural -> Bool
-propPellEquation n =
-    Quadratic.isSquare n || a * a == n * b * b + 1
+propPellEquation :: Natural -> Natural -> Bool
+propPellEquation n ip =
+    a * a == n * b * b + 1
   where
-    (a,b) = Pell.solution n
-
-{-
-np = (0 :: Natural)
-ps = ([] :: [Natural])
-qs = ([] :: [Natural])
-n = np + 2
-r = Modular.ring n
-p = Polynomial.fromCoefficients r (map (Ring.fromNatural r) ps)
-q = Polynomial.fromCoefficients r (map (Ring.fromNatural r) (qs ++ [1]))
--}
+    (a,b) = Pell.solutions n !! i
+    i = fromIntegral (if Quadratic.isSquare n then 0 else ip)
 
 check :: QuickCheck.Testable prop => String -> prop -> IO ()
 check desc prop =
@@ -592,5 +583,5 @@
        check "Polynomial quotient remainder" propPolynomialQuotientRemainder
        check "Polynomial quotient remainder monic"
          propPolynomialQuotientRemainderMonic
-       check "Pell equation solution" propPellEquation
+       check "Pell equation solutions" propPellEquation
        return ()