Question

- what describe the Collatz conjecture and why can being considered importantly ?
how can it proving ?

Answer 1

Start with a positive integer. If it is even, halve it, else
multiply by 3 and add 1.

Important (perhaps) for it's relationship to complexity and undecidability.

Apparently we don't have the necessary math techniques to prove it which puts it in the same class as p np problem.

Answer 2

The conjecture states that following the rule above will produce a sequence that terminates in 1.