code for http://olimex.wordpress.com/2013/05/24/weekend-programming-challenge-issue-10/

wpc_10.hs

-- using Haskell's library for rational numbers, which stores a rational as
-- a pair of integer numbers (not limited to 32 or 64 bits); hence able to do
-- exact arithmetic etc up to high numbers
import Data.Ratio

-- the core function: spits out a list of ascending n for the fractions
-- works by reducing (a/b) to 1/ceil(b/a) + ...
fractionize t
 | t == 0     = []
 | diff >= 0  = next : fractionize diff
 where
   diff = t - 1 % next
   next = ceiling (1 / t)


-- examples
--   fractionize (6 % 7)           =====> [2,3,42]
--   fractionize (10242 % 1414244) =====> [139,20927,494331640,341895644508855255,2674143744440687043922347253562499240]
---  check: sum (map (1/) [139,20927,494331640,341895644508855255,2674143744440687043922347253562499240]) - 10242 / 1414244 (gives 0)

wpc_10_test.hs

-- add this code to the above, and run "main" to run 
-- various tests

-- some testing/demonstration functions
-- running over a n * m grid, where i < j 
chk f n m
 = [ let ns = f (i%j) in (i,j, ns, sum (map (1%) ns) == i%j)
   | i <- [1 .. n], j <- [1..m], i < j ]

-- nice formatting etc
tst f n
 = putStrLn
 $ case [ show (i,j,ns) | (i,j,ns,False) <- chk f n n ] of
     [] -> "No problems"
     fs -> unlines $ "FOUND BAD:" : fs

-- run for numbers up to 200 
main = tst (fractionize) 200