list up rational numbers p such that sqrt(p), sqrt (p - 5), sqrt (p + 5) are all rational.

README.md

list up rational numbers p such that sqrt(p), sqrt (p - 5), sqrt (p + 5) are all rational.

*Main> take 2 answer
[1681 % 144,11183412793921 % 2234116132416]

find.hs

answer =
  map
  conversion
  (filter
   (\(x, y, z) -> test x y)
   pythagorean_triples)

conversion :: (Integer, Integer, Integer) -> Rational
conversion (x, y, z) =
  toRational (z * z) / (toRational (4 * x * y) / toRational 10)

test :: Integer -> Integer -> Bool
test x y =
  (w `mod` 10) == 0 &&
  is_squre (
    floor ((fromInteger w) / 10))
  where
    w = x * y

pythagorean_triples =
  filter
  (\(x, y, z) -> gcd x y == 1)
  [(m * m - n * n, 2 * m * n, m * m + n * n) | m <- [1..], n <- [2..m-1]]

is_squre :: Integer -> Bool
is_squre a =
  a == (floor . sqrt . fromInteger) a ^ 2