(*
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^(2) + b^(2) = c^(2)

For example, 3^(2) + 4^(2) = 9 + 16 = 25 = 5^(2).

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
*)

(* is a pythagorean triplet *)
let ptriplet a b c = ( a*a + b*b = c*c );;

let rec search a b =
  if (a>332) then 0 else
  if (b>499) then search (a+1) (a+1) else

  let c=(1000-a-b) in
    if ((a*a)+(b*b)=(c*c))
    then (a*b*c)
    else search a (b+1)
;;

Printf.printf "%d\n" (search 0 0)