Timeline for How would one go about solving this conjecture concerning exponential Diophantine equations?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2023 at 17:05 | comment | added | John Eaton | I have come across a huge misstep in my paper. Therefore, I would like to close this question. I will not delete it, but I no longer am seeking answers for the above question. | |
| Aug 27, 2023 at 18:03 | comment | added | John Eaton | It’s the same process, $(-1) -> (-1)$. I.e $\frac{( 3(-1) + 1)}{2} = \frac{3}{2}(-1) + \frac{3 - 2}{2} = -1$ . Thus, $ m = n = a = b = c = 1 $. I’m sure you can figure out the other fixed points. | |
| Aug 22, 2023 at 14:14 | comment | added | Robert Frost | Thanks @JohnEaton for giving me $(1,2)$ which narrows it down a bit but are you able to indicate how the solutions $(-1)$ and $(-5,-7,-10)$ are represented in your $a,b,c,m,n$? | |
| Jul 29, 2023 at 20:46 | comment | added | John Eaton | For example, put $k =1$ , then we can set $a = b =1$ , $c = 2$ , $m =1$ , and $n = 2$. This corresponds to the shortened Collatz map that takes $1$ to $2$ and $2$ to $1$. | |
| Jun 28, 2023 at 10:04 | comment | added | Robert Frost | @JohnEaton that won't work for me. How are e.g. the solutions $(-1)$ and $(1,2)$ represented in your equation? How is the solution $(-5,-7,-10)$ represented? | |
| Jun 6, 2023 at 16:42 | comment | added | John Eaton | Please take a look at my paper linked above @it'sahirecarbaby | |
| Jun 5, 2023 at 12:05 | comment | added | Robert Frost | How do the values of $a,b,c,m,n,k$ relate to "solutions" to the Collatz conjecture? Are we to assume you are proposing every solution to your equation represents a loop containing $m+n$ steps, of which $m$ are odd and $n$ even? If so, the number of solutions to your equation for which $k\in\Bbb Z_2^\times$ (i.e. a 2-adic unit) are enumerated by the base $2$ Lyndon words of length $n+m$. This is because the functions orbits are topologically conjugate to the tent map. | |
| Apr 17, 2023 at 2:38 | comment | added | John Eaton | I’ve also tried looking at S-unit equations. Still doing some research though. | |
| Apr 10, 2023 at 11:41 | history | edited | John Eaton | CC BY-SA 4.0 |
I got rid of all the subscripts in favor of readability.
|
| Apr 10, 2023 at 11:36 | comment | added | John Eaton | I’ll add the link to vixra and my Quora space. Vixra: vixra.org/abs/2304.0050. My Quora space : mathscape.quora.com/… | |
| Apr 10, 2023 at 6:12 | comment | added | SARTHAK GUPTA | I am interested how you reduced to this EDE. | |
| Apr 10, 2023 at 5:49 | comment | added | user44143 | I fixed one formatting issue here, but all the subscripts make this hard to read, just as with your previous question. | |
| Apr 10, 2023 at 5:42 | history | edited | user44143 | CC BY-SA 4.0 |
put key equation on its own line
|
| Apr 9, 2023 at 23:09 | history | asked | John Eaton | CC BY-SA 4.0 |