text: where  denotes the resultant of a and b. In this form of Bézout's identity, there is no denominator in the formula. If one divides everything by the resultant one gets the classical Bézout's identity, with an explicit common denominator for the rational numbers that appear in it.
  Pseudocode
  To implement the algorithm that is described above, one should first remark that only the two last values of the indexed variables are needed at each step. Thus, for saving memory, each indexed variable must be replaced by just two variables.
  For simplicity, the following algorithm (and the other algorithms in this article) uses parallel assignments. In a programming language which does not have this feature, the parallel assignments need to be simulated with an auxiliary variable. For example, the first one,
  (old_r, r) := (r, old_r - quotient * r)
  is equivalent to
  prov := r;
  r := old_r - quotient × prov;
  old_r := prov;
  and similarly for the other parallel assignments.
  This leads to the following code:
  function extended_gcd(a, b)
  (old_r, r) := (a, b)
  (old_s, s) := (1, 0)
  (old_t, t) := (0, 1)
  while r ≠ 0 do
  quotient := old_r div r
  (old_r, r) := (r, old_r − quotient × r)
  (old_s, s) := (s, old_s − quotient × s)