Brute force analogue of computation in orders.hs (https://gist.github.com/viviag/cfe9b791d57e208a97369919baf968cb)

orders0.hs

type Order = Integer
type Element = Integer

order :: Order -> Element -> Order
order p elem = order' p elem elem 1
  where
    order' _ 1 _ ord = ord
    order' p power elem ord = order' p (power*elem `mod` p) elem (ord+1)

elemsOfOrder :: Order -> Order -> [Element]
elemsOfOrder p d = filter (\elem -> order p elem == d) [1..p-1]

main :: IO ()
main = do
  putStr "Insert modulus: "
  p <- read <$> getLine
  putStr "Insert order of element: "
  ord <- read <$> getLine
  print $ elemsOfOrder p ord