From 9db0008777cc4cd9f07e14a3458e3d903e3cc4f6 Mon Sep 17 00:00:00 2001
From: Determinant <ted.sybil@gmail.com>
Date: Mon, 29 May 2017 13:29:11 -0400
Subject: finish vol 4

---
 31-41/31.hs |  4 ++++
 31-41/32.hs |  5 +++++
 31-41/33.hs |  9 +++++++++
 31-41/34.hs | 11 +++++++++++
 31-41/35.hs |  9 +++++++++
 31-41/36.hs | 15 +++++++++++++++
 31-41/37.hs | 19 +++++++++++++++++++
 31-41/39.hs |  5 +++++
 31-41/40.hs | 10 ++++++++++
 31-41/41.hs | 16 ++++++++++++++++
 10 files changed, 103 insertions(+)
 create mode 100644 31-41/31.hs
 create mode 100644 31-41/32.hs
 create mode 100644 31-41/33.hs
 create mode 100644 31-41/34.hs
 create mode 100644 31-41/35.hs
 create mode 100644 31-41/36.hs
 create mode 100644 31-41/37.hs
 create mode 100644 31-41/39.hs
 create mode 100644 31-41/40.hs
 create mode 100644 31-41/41.hs

diff --git a/31-41/31.hs b/31-41/31.hs
new file mode 100644
index 0000000..d6d53a9
--- /dev/null
+++ b/31-41/31.hs
@@ -0,0 +1,4 @@
+isPrime :: Int -> Bool
+
+isPrime 1 = False
+isPrime x = and $ map (\y -> x `mod` y /= 0) $ fst $ span (\y -> y * y <= x) [2..]
diff --git a/31-41/32.hs b/31-41/32.hs
new file mode 100644
index 0000000..585039d
--- /dev/null
+++ b/31-41/32.hs
@@ -0,0 +1,5 @@
+myGCD :: Int -> Int -> Int
+
+
+myGCD a 0 = abs a
+myGCD a b = myGCD b (a `mod` b)
diff --git a/31-41/33.hs b/31-41/33.hs
new file mode 100644
index 0000000..52bebbb
--- /dev/null
+++ b/31-41/33.hs
@@ -0,0 +1,9 @@
+myGCD :: Int -> Int -> Int
+
+
+myGCD a 0 = abs a
+myGCD a b = myGCD b (a `mod` b)
+
+coprime :: Int -> Int -> Bool
+
+coprime a b = myGCD a b == 1
diff --git a/31-41/34.hs b/31-41/34.hs
new file mode 100644
index 0000000..fe542a2
--- /dev/null
+++ b/31-41/34.hs
@@ -0,0 +1,11 @@
+import Data.List (foldl')
+
+myGCD :: Int -> Int -> Int
+
+
+myGCD a 0 = abs a
+myGCD a b = myGCD b (a `mod` b)
+
+totient :: Int -> Int
+
+totient x = foldl' (\acc y -> acc + if myGCD x y == 1 then 1 else 0) 0 [1..x]
diff --git a/31-41/35.hs b/31-41/35.hs
new file mode 100644
index 0000000..185d024
--- /dev/null
+++ b/31-41/35.hs
@@ -0,0 +1,9 @@
+primeFactors :: Int -> [Int]
+
+primeFactors x = factor x primes
+    where primes = filterPrime [2..]
+          filterPrime (p:xs) = p:filterPrime [x | x <- xs, x `mod` p /= 0]
+          factor x l@(p:xs)
+            | p > x = []
+            | x `mod` p == 0 = p:factor (x `div` p) l
+            | otherwise = factor x xs
diff --git a/31-41/36.hs b/31-41/36.hs
new file mode 100644
index 0000000..cb9d09a
--- /dev/null
+++ b/31-41/36.hs
@@ -0,0 +1,15 @@
+import Data.List (group)
+
+primeFactors :: Int -> [Int]
+
+primeFactors x = factor x primes
+    where primes = filterPrime [2..]
+          filterPrime (p:xs) = p:filterPrime [x | x <- xs, x `mod` p /= 0]
+          factor x l@(p:xs)
+            | p > x = []
+            | x `mod` p == 0 = p:factor (x `div` p) l
+            | otherwise = factor x xs
+
+primeFactorsMult :: Int -> [(Int, Int)]
+
+primeFactorsMult x = [(head l, length l) | l <- group $ primeFactors x]
diff --git a/31-41/37.hs b/31-41/37.hs
new file mode 100644
index 0000000..ead0514
--- /dev/null
+++ b/31-41/37.hs
@@ -0,0 +1,19 @@
+import Data.List (group, foldl')
+
+primeFactors :: Int -> [Int]
+
+primeFactors x = factor x primes
+    where primes = filterPrime [2..]
+          filterPrime (p:xs) = p:filterPrime [x | x <- xs, x `mod` p /= 0]
+          factor x l@(p:xs)
+            | p > x = []
+            | x `mod` p == 0 = p:factor (x `div` p) l
+            | otherwise = factor x xs
+
+primeFactorsMult :: Int -> [(Int, Int)]
+
+primeFactorsMult x = [(head l, length l) | l <- group $ primeFactors x]
+
+phi :: Int -> Int
+
+phi x = foldl' (\acc (p, m) -> acc * (p - 1) ^ m) 1 (primeFactorsMult x)
diff --git a/31-41/39.hs b/31-41/39.hs
new file mode 100644
index 0000000..68909d7
--- /dev/null
+++ b/31-41/39.hs
@@ -0,0 +1,5 @@
+primesR :: Int -> Int -> [Int]
+
+primesR l r = takeWhile (<= r) $ dropWhile (< l) primes
+    where primes = filterPrime[2..]
+          filterPrime (p:xs) = p:filterPrime [x | x <- xs, x `mod` p /= 0]
diff --git a/31-41/40.hs b/31-41/40.hs
new file mode 100644
index 0000000..9d9b2f7
--- /dev/null
+++ b/31-41/40.hs
@@ -0,0 +1,10 @@
+isPrime :: Int -> Bool
+
+isPrime 1 = False
+isPrime x = and $ map (\y -> x `mod` y /= 0) $ fst $ span (\y -> y * y <= x) [2..]
+
+goldbach :: Int -> (Int, Int)
+
+goldbach x = head [(a, b) | a <- primes, let b = x - a, isPrime b]
+    where primes = filterPrime[3..]
+          filterPrime (p:xs) = p:filterPrime [x | x <- xs, x `mod` p /= 0]
diff --git a/31-41/41.hs b/31-41/41.hs
new file mode 100644
index 0000000..16fd51f
--- /dev/null
+++ b/31-41/41.hs
@@ -0,0 +1,16 @@
+isPrime :: Int -> Bool
+
+isPrime 1 = False
+isPrime x = and $ map (\y -> x `mod` y /= 0) $ fst $ span (\y -> y * y <= x) [2..]
+
+goldbach :: Int -> (Int, Int)
+
+goldbach x = head [(a, b) | a <- primes, let b = x - a, isPrime b]
+    where primes = filterPrime[3..]
+          filterPrime (p:xs) = p:filterPrime [x | x <- xs, x `mod` p /= 0]
+
+goldbachList :: Int -> Int -> [(Int, Int)]
+goldbachList' :: Int -> Int -> Int -> [(Int, Int)]
+
+goldbachList l r = map goldbach $ filter even $ dropWhile (< 4) [l..r]
+goldbachList' l r i = filter (\(a, b) -> a > i && b > i) $ goldbachList l r
-- 
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