Writing a research proposal in mathematics for graduate school
My recommendation is to try to ask some current students if you can see their proposals.  Obviously, what they did can't be all that terrible.  

More generally, I would agree that methodology is not a extremely well defined concept in mathematics, but you can write something intelligent about it anyways.  How are you going to approach the problem?  Are there special cases that might be illuminating?  Stepping stone lemmata you might get to before the whole proof?  What areas of mathematics do you hope to use?  Unfortunately, I can't speak for the system in Italy, but certainly in the US with such research proposals, the main point is to see if the candidate can write about and analyze mathematics in a cogent way, not the details of the problem.