Hello everyone,

I'm sure this problem can interest some of you. I need the answers for a research project. I currently don't know the answers.

Let be two positive integers.

we consider this number

Let denote the sorted list of values which can be reached by .

For example :

Now here come the questions :

Let be an integer.

- What is the value of ?

- How many different couples verify ?

Let denote this number .

- What is ?

Let denote this last sum.

- For given, find the corresponding . This last one should not be too hard to find if is found as an analytic function of (we just need to inverse it then), but I am not sure it's possible .

Many thanks for your help.