[QUOTE=dabler;549598]After less than a year, I managed to verify all numbers below 2[SUP]68[/SUP] in this way. For those who are interested, the results are presented in [URL="https://rdcu.be/b5nn1"]this article[/URL].[/QUOTE]
Thanks for the link!

[QUOTE=moebius;549605]Poll:
Which of the previous avatars looks most like a mugshot from sheriff's department?[/QUOTE]
Robert Gerbicz's one? :lol:

Has anyone studied the behavior of the Collatz function in finite fields?

[QUOTE=dabler;565779]Has anyone studied the behavior of the Collatz function in finite fields?[/QUOTE]

[url]https://scholar.google.com/scholar?hl=en&as_sdt=0%2C33&q=Collatz+%22finite+field%22&btnG=[/url]

[QUOTE=CRGreathouse;565890][url]https://scholar.google.com/scholar?hl=en&as_sdt=0%2C33&q=Collatz+%22finite+field%22&btnG=[/url][/QUOTE]

??

[QUOTE=dabler;565931]??[/QUOTE]
That was a kind and gentle variation of the "LMGTFY" answer.
What you asked for - is all there. All that remains to be done is ...[I] just read it![/I]

[QUOTE=Batalov;565971]That was a kind and gentle variation of the "LMGTFY" answer.
What you asked for - is all there. All that remains to be done is ...[I] just read it![/I][/QUOTE]

Yes. Basically, there was too much research for me to post just one or two papers, and not enough in your question to narrow the field down, so I just linked to a search showing the sorts of papers that are out there. Following authors and references forward and backward should yield more.

Unc, thanks for add all Collatz threads.

Posting to [U]solely[/U] ask people to respond to your post in another thread is not a polite thing to do.

please remove.
sorry

You can forget all the even numbers.
You can also remove all 5's on each step.
Or anything finite list of prime numbers.
The equations what are finally solved are absolutly equivalents.
If one is solved, the other also.

You can up with 5n+1, and down removing 2s and 3s.
Is the same eqn.
Eqn solvable, ONE reached.
Eqn not solvable, ONE never reached.

The conjecture is true, dont worry.
I post one algebraic equivalence.
Best try to solve it.

Colltatz is nice.
Is like a box with Galois theory, succesions, and caotic atractors.
Im absolutly sure that Collatz conjecture is today solvable.
Dont believe pesimist words.