BLD added solutions 1-4

Author: eigenfoo

euler001.hs

@@ -0,0 +1,2 @@
+main = print $ sum $ filter multiple3or5 [1..999]
+    where multiple3or5 = (\n -> n `rem` 3 == 0 || n `rem` 5 == 0)

euler002.hs

@@ -0,0 +1,10 @@
+import Data.List
+
+main = print $ sum [x | x <- takeWhile (< 4000000) fibs, even x]
+    where fibs = unfoldr (\(a, b) -> Just (a, (b, a+b))) (1, 1)
+
+{-
+It turns out there is an extremely elegant, recursive way of generating the
+Fibonacci numbers using zipWith:
+    fibs = 1 : 1 : zipWith (+) fibs (tail fibs)
+-}

euler003.hs

@@ -0,0 +1,9 @@
+main = print $ maximum $ prime_factors 600851475143
+
+prime_factors :: (Integral a) => a -> [a]
+prime_factors 1 = []
+prime_factors n
+    | factor == [] = [n]
+    | n < (head factor)^2 = [n]   -- stop searching if sqrt n < head factor
+    | otherwise = factor ++ prime_factors (n `div` (head factor))
+        where factor = take 1 [x | x <- [2..n-1], n `rem` x == 0]

euler004.hs

@@ -0,0 +1,3 @@
+main = print $ maximum palindromes
+    where palindromes = [x*y | x <- [999,998..1], y <- [999,998..1],
+                               (reverse $ show (x*y)) == (show (x*y))]