...like the following without AI assistance ? Looking for differentiable solutions! The solution is not to be found in the books by Aczel or Small: L(x)*L(y) = L(2*x*y + x + y). (I know the stressful solution from my notes - the ones made with pen and paper.)

Is there a way in Maple to categorize functional equations into specific classes (e.g., Cauchy type) - and thereby identify corresponding solution methods - much like how Maple handles the solving of ordinary differential equations?

While practicing with the "identify" command, I came across the question:

Does Maple offer a way to determine the generating rule for a sequence of numbers given by a finite initial segment?

Here is a riddle for this:

The sequences {s_n} = 1/1; 1/2; 1/3; ... and {t_n} = 0/1; 1/2; 2/3; 3/4; ... have the formation rules

s_n = 1/n and t_n = (n-1)/n.
What is the formation rule for the sequence {u_n} = {s_n; t_n} formed by alternating between the two?
Note: The solution is not u_2n = t_n and u_(2n−1) = s_n. Rather, the goal is to find a single, unified formation rule u_n that yields the terms of the combined sequence for n = 1; 2; 3; ...

How would one go about querying AI in Maple?

With thanks for the advice regarding quadratic Diophantine equations and tabulation, here is a little puzzle:
For a rectangular cuboid, the length of the space diagonal is known to be 90 cm and its surface area 8800 cm². Determine its integer edge lengths.

In the attached file, I would like to create a table of values ​​(k,f(k),g(k)) for the functions f and g for, e.g., k=1..10. I would appreciate your help with this, as f and g refer to reciprocity in their expressions.

test.mw

How to solve this Diophantine equation?

x^2-12*x*y+6*y^2+4*x+12*y-3=0    ?

I would appreciate some advice.