puzzle.hs

import Data.SBV

p :: Goal
p = do a  <- sInteger "a"
       b  <- sInteger "b"
       ab <- sInteger "ab"

       constrain $ a*a - b*b .== 21
       constrain $ a*a + b*b .== 29

       constrain $ ab .== a*b

{-
*Main> main
Solution #1:
  a  =  -5 :: Integer
  b  =   2 :: Integer
  ab = -10 :: Integer
Solution #2:
  a  =  5 :: Integer
  b  =  2 :: Integer
  ab = 10 :: Integer
Solution #3:
  a  = -5 :: Integer
  b  = -2 :: Integer
  ab = 10 :: Integer
Solution #4:
  a  =   5 :: Integer
  b  =  -2 :: Integer
  ab = -10 :: Integer
Found 4 different solutions.
-}
main :: IO ()
main = print =<< allSat p