A new short mathematical letter has been published about the Collatz conjecture. It gives the only possible five expressions of natural numbers which can respect the Collatz conjecture. Can you find the counter-example with this result or prove that the Collatz conjecture is true ?

Here is the link:

https://www.researchgate.net/publication/377746599_The_only_five_expressions_of_numbers_which_respect_the_Collatz_conjecture