I am not sure if I should ask this question here or somewhere else.

**Background**: I was searching through random mathematics paper that are related to cryptography and I came across this paper (page 3). I just read the abstract and algorithm itself, I don't understand Chinese. It offers new method to find a Modular inverses. It has some interesting properties that I observed:

- during each step iteration of the loop: $x_{11} * x_{22} + x_{12} * x_{21} = m$ which is good to validate the result during each iteration
- algorithm terminates in even number of steps for some unknown reason

In abstract section, author says this method was invented by this mathematicians.

**I have two unrelated questions**:

- why this algorithm always terminates in even number of steps (or number of iterations of the loop is always even)
- was this algorithm invented before extended-euclidean algorithm that we use today