S-Unit questions

[hermann@stamm-wilbrandt.de]

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.