/sci/ - Science & Math

>>12523392
If you're implying you found the relation on SE, please share the link.

I got at it by trying to recast an unsolved number theoretic problem into an algebra context.
Namely there's only two solutions known to
[math] \dfrac{x^m - 1}{x-1}=\dfrac{y^n - 1}{y - 1} [/math]

e.g.
[math] \dfrac{5^3-1}{5-1}=\dfrac{2^5-1}{2-1}=31 [/math]

and a second one, and the conjecture is that those are all of them, see
https://en.wikipedia.org/wiki/Goormaghtigh_conjecture

I recast the condition as one of a rep of sl(2), where this says that the following difference is diagonal
[math]\left(
\begin{array}{cc}
x & h \\
0 & 1 \\
\end{array}
\right)^m-\left(
\begin{array}{cc}
y & h \\
0 & 1 \\
\end{array}
\right)^n[/math]
(the condition is saying that the top right component vanishes for any h)

>>12524601
How pure are we talking?
And do you want it to be actually actually usable for you later on (something you end up using)?

I bought this 100$ drone (pic related) that some Indian guy on youtube will do a basic course on and I plan to overcomplicate by implementing some routines in some-close-to-the-math algorithms for it's mechanics and dynamics.

You're welcome to join my leisure effort. One might indeed also port the stuff to a more mathematical language (I'm interested in Idris)