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.