Re: S-Unit questions

[hermann@stamm-wilbrandt.de]

Small corrections:

The unknown GP command is bnfuniteqn().

> ±2^{a1}*3^{b1}±2^{a2}*3^{b2}=1
>
> One solution is 9/8−1/8=1 with a1=3, b1=2, a2=3, b2=0 ...
a1=a2=-3

Regards,

Hermann.

On 2026-03-12 14:58, hermann@stamm-wilbrandt.de wrote:
> I had discussions with AIs on a number theoretic question I am 
> interested in.
>
> One made the connection with S-Units
> https://en.wikipedia.org/wiki/S-unit
> and there it is stated this is a topic of algebraic number theory.
>
> I tried to understand, but just finished 1st semester of Mathematics
> at age of 60 at University of Heidelberg with Linear Algebra 1 and 
> Analysis 1.
>
> Plan is to attend algebraic number theory 1 after Linear Algebra 2 and
> Algebra 1 and 2 end of next year. Nevertheless I want to understand now
> how PAR/GP can help me with my current problem.
>
>
> But first the simple problem of solving diophantine equations with
> PAR/GP and S-Units.
> Gemini gave me script using thueinit, but that errored when passing x-1 
> for ℤ.
>
> On error message it explained that linear polynomial has too low
> degree for thueinit.
> And to use a script with "bnfisunit()" — but current GP does not know
> this command.
>
> So how to solve this equation using PARI/GP with its Baker(?) 
> algorithm?
>
> ±2^{a1}*3^{b1}±2^{a2}*3^{b2}=1
>
> One solution is 9/8−1/8=1 with a1=3, b1=2, a2=3, b2=0 ...
>
>
> Regards,
>
> Hermann.