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

...Diophantine equation:

x^2-12*x*y+6*y^2+4*x+12*y-3=0    ?

I would appreciate some advice.

A bundle of planes is here defined as the set of all planes in Cartesian (x, y, z)-space that intersect along the same straight line. This line is commonly referred to as the axis of the bundle. Is there an efficient method in Maple to model a bundle of planes in a simple, symbolic way?
The background to my request for advice is the following problem (for those interested in the puzzle), dating back to 1965:
Let a surface be given in Euclidean space. Suppose that every planar section of the surface is a circle, provided the section contains more than one point. Prove that the surface is a sphere.

edited:

Simple deductions are sufficient to solve the puzzle. Complex calculations are not necessary.

A Blog Post reminded me of an old problem from my Mathcad-days:
Given a torus and two points, P and Q, on its surface, calculate and graphically represent the shortest path from P to Q.

edited:
Can Mathcad worksheets (MC14) be converted into functional worksheets for Maple?

In the attached file, I want to represent a mixed polynomial in x, y, and z as the sum of squares from bracketed expressions. I know the result. But how do I do this in Maple? The help text didn't help me :-( .

test.mw