(********************************************************************)
(*  OCaml code from the book ``Learn Programming with OCaml''       *)
(*  See https://usr.lmf.cnrs.fr/lpo/                                *)
(*                                                                  *)
(*  Sylvain Conchon and Jean-Christophe Filliâtre                   *)
(*  Copyright 2025 Université Paris-Saclay and CNRS                 *)
(*                                                                  *)
(*  Openly licensed via CC BY SA 4.0                                *)
(*  See https://creativecommons.org/licenses/by-sa/4.0/deed.en      *)
(********************************************************************)

(* Program 79 on page 345
   The extended Euclidean algorithm *)

let rec extended_gcd x y =
  if y = 0 then
    (1, 0, x)
  else
    let q = x / y in
    let (u, v, g) = extended_gcd y (x - q * y) in
    (v, u - q * v, g)

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