The attached file "test" asks for the largest power of two contained as a factor in a term. This is easily solved using "simplify." How can this be achieved using factorization?

test.mw

Thanks for the help with the recursion problem, here's a very challenging problem for the weekend ;-). It should be solvable in Maple, at least for examples. I only know of one very theoretical, unfinished solution that I'm still working on:
Given a closed convex curve in the Euclidean plane. It is multiply continuously differentiable, and the curvature is also continuous.
Then there are at least three pairs of points on the curve with the following property:
The tangents at the points of each pair are parallel to each other, and the curvatures are equal.

According to the attached file "test" I would like to determine the limit of the function f(n,x) for n-->00 as an exercise. I'm asking for advice on using "rsolve". I also want to calculate the limit of sqrt((n/3))*f(n,x) for n-->00 using f(n,x) from the file "test". I also need help with this. (This isn't a school assignment ;-).)

test.mw

Using the attached problem, I want to calculate a term with a constraint that m is not equal to n. How do I insert general constraints into Maple?

test.mw

I'm doing something wrong again in the attached file. Please advise.

test.mw