text: Also it means that the algorithm can be done without integer overflow by a computer program using integers of a fixed size that is larger than that of a and b.
  Example
  The following table shows how the extended Euclidean algorithm proceeds with input  and . The greatest common divisor is the last non zero entry,  in the column "remainder". The computation stops at row 6, because the remainder in it is . Bézout coefficients appear in the last two entries of the second-to-last row. In fact, it is easy to verify that . Finally the last two entries   and  of the last row are, up to the sign, the quotients of the input  and  by the greatest common divisor .
  Proof
  As  the sequence of the  is a decreasing sequence of nonnegative integers (from i = 2 on). Thus it must stop with some  This proves that the algorithm stops eventually.
  As  the greatest common divisor is the same for   and  This shows that the greatest common divisor of the input  is the same as that of  This proves that  is the greatest common divisor of a and b. (Until this point, the proof is the same as that of the classical Euclidean algorithm.)