By "abstract" I meant "with some form, but without concrete or specific value" and in "I want to solve this for some n, but I can't or won't tell you what n is." Mathematica and WolframAlpha sometimes seem to only have less powerful methods available when solutions are desired in terms of variables that are not given specific concrete values for n.

Thank you for providing the desired form of your solution. That helped. Getting Mathematica or WolframAlpha to provide a solution in a specific desired form has often been more difficult than just getting it to provide a correct solution in any form.

I realize that people often want compact solutions in the form that they desire. Unfortunately I have no idea how to tell it to provide your solutions in the form that you desire. When asking it to provide solutions for u and v, I have not seen it provide solutions where u is left in part of the solution, not unless the problem is so difficult that there is no way to solve for u. What I have seen is that it keeps pounding on the solution until there is no u or v left in the right hand side of either equation.