module SqTr where

-- Make a square number
squareNumber :: Integer -> Integer
squareNumber = (^2)

-- Make a triangle numnber
triNumber :: Integer -> Integer
triNumber x = fromIntegral (round (x' * (x' + 1) * 0.5)) :: Integer
  where x' = fromInteger x

stMatch x = squareNumber x == triNumber x

squares = [(x, x^2) | x <- [1..]] :: [(Int,Int)]

triangles = [(round x :: Int, round (x * (x + 1) * 0.5) :: Int) | x <- [1..]]

matches sqrs tris = [(x, y, s) | (x, s) <- sqrs, (y, t) <- tris, s == t]

squareTriangleNumbers = [(x,y) | x <- [1..], y <- [1..], stn x y == 0]
  where stn x y = (2 * x^2) - (y^2) - y

--
-- n^2 = m (m+1)
--       -------
--           2
--
--
--
-- 2n^2 = m^2 + m
--
--
-- 0 = 2n^2 - m^2 - m