Add solution for problem 44.

Problem044.hs

@@ -0,0 +1,19 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+import Euler
+
+-- Pentagonal numbers are generated by the formula, P[n]=n(3n−1)/2.
+--
+-- Find the pair of pentagonal numbers, P[j] and P[k], for which their sum and
+-- difference are pentagonal and D = |P[k] − P[j]| is minimised; what is the value
+-- of D?
+
+pentagonals = map (\n -> n * (3*n - 1) `div` 2) [1..]
+isPentagonal x = let n = (sqrt (24 * fromIntegral x + 1) + 1) / 6 in n == fromIntegral (floor n) && n > 0
+
+main = print $ minimum $ do
+  -- Assumption: The solution will not require considering pentagonals over 10^7.
+  b <- takeWhile (< 10000000) pentagonals
+  a <- takeWhile (< b) pentagonals
+  guard $ isPentagonal (a + b)
+  guard $ isPentagonal (b - a)
+  return $ b - a