A program to perform modular arithmetic

Write a computer program to add and multiply mod n, for any n given as input. The output of these operations should be the least residues of the sums and products of the two integers. Also include the feature that if , an integer  between 0 and  such that  mod n may be printed on request.

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mod :: Integer -> Integer -> Integer mod a n'  | a < 0     = mod (a+n) n  | a > n     = mod (a-n) n  | otherwise = a  where n = abs n'   plusMod :: Integer -> Integer -> Integer -> Integer plusMod n a b = mod (a+b) n   timesMod :: Integer -> Integer -> Integer -> Integer timesMod n a b = mod (a*b) n   invMod :: Integer -> Integer -> Maybe Integer invMod a n  = if (gcd a n) /= 1     then Nothing     else Just $ foo $ fst $ bezout a n    where foo k = if k < 0 then (k+n) else k