modulo :: Int -> Int -> Int
modulo x y =
    x - (x `div` y) * y



primeFactors :: Int -> [Int]
primeFactors x =
    let p = (\x e c -> if (x == 1)
                       then (reverse c)
                       else if (x `modulo` (head e) == 0)
                            then p (x `div` (head e)) e ((head e) : c)
                            else p x (tail e) c)
    in p x euler []



euler :: [Int]
euler =
    let f = (\list -> (head list) : (f (filter (\x -> x `modulo` (head list) /= 0) list)))
    in f [2..]



isPowerOf :: Int -> Int -> Bool
isPowerOf x y =
    case (compare x y) of
        LT -> False
        EQ -> True
        GT -> if (x `modulo` y == 0) then isPowerOf (x `div` y) y else False