@salim-barzani 

@salim-barzani I updated the answer to include the fsolve commands, using search ranges based on the plot. Each case with different numerical parameters will be different. There are two examples. The solutions are at the intersections of the red and blue curves.

I don't know why it was deleted, but in the past I have deleted ones that are duplicates and instead of telling the person that it was deleted because it was a duplicate they get told it was spam, which is clearly a problem with the system.

At least in Windows, the alt key shows menu shortcuts, e.g., F pops up above the file menu, then alt-F opens the file menu and shows, e.g., O for open and FO for file open. This is common Windows behaviour, but is an alternative to the ctrl- shortcuts.

@MAXR There is a difference between the dots. Anyway, I am currently traveling so perhaps someone else can help you.

@MAXR Please upload your revised version.

@sand15 Some years ago I tried to get my university to renew its site licence, which was very reasonably priced. At the time they were in financial cutback mode, so it wasn't possible. But I did talk to the mathematicians, many of whom had used Maple in the past, but now they have all (but one) changed to SageMath.

A lot of this is driven by cost, and free open source alternatives are now available. Similarly, many engineering departments are changing from matlab to python, again as a cost-saving measure.

So I think the nice interface is an attraction for teaching mathematics and that is a good market. I keep answering questions on stackexchange using Maple, in the hope that is some good advertising. 

You have used a dot "." (matrix multiplication) instead of "*", so you should start by fixing that.

@janhardo I don't understand what you are saying. Are you making some fine distinction between a proof and an algorithm? Many proofs are algorithmic.

@janhardo You could, but the standard way would be via the characteristic polynomial as @Rouben Rostamian used (and presumably Maple's rsolve uses).

@sand15 In my view, the drop is due to ai. The same thing has happened on stack exchange (in say, math and chemistry sites that I interact with). On stackoverflow there were steady Maple questions until October 2024, then only 3 since, so Mapleprimes is doing better.

I also don't buy the point that because there are now more questions/answers on Mapleprimes, that people are just searching the site; in my experience the search function is poor; I cannot always find questions I know I have answered.

The older community being more experienced and therefore asking fewer question also is not correct, since these older people mainly answer questions rather than ask them. 

Typical ai rambling...

@Rouben Rostamian  "But that doesn't prove that the conclusion holds for arbitrary n." I took a recurrence (with only integer solutions), solved it, and showed (with the final step from @acer) that it was equal to ans. You took ans and derived a recurrence with integer solutions.  These are quivalent ways of doing the same thing, with no limitation on n. The fact that I guessed the recurrence from 25 values was not enough, but if the recurrence gives ans then that validates it for all n.

@Alfred_F @acer That's nice work with simplify. I didn't try very hard here since in general Maple is not so good with symbolic exponents; evala is made for this type of field extension manipulation for integer n, but not for symbolic n. I am surprised therefore that you didn't need an assumption.

And @Alfred_F, your questions often push the boundaries in this respect, so that is fun.

With no information, it is hard to help. If you are using Windows you will need to run as administrator to get it to install correctly. Other than that I have never had any installation issues. 

This is a known issue with the context panel - see a recent Mapleprimes question. It has been reported and is being fixed. There is a facility to change the number of decimal places displayed for the whole worksheet. See File - options (button bottom right) - precision -round screen display to XX decimal places.