Scrum Roles

They can't. The Scrum Guide doesn't explicitly talk about that, but:

1) Scrum moved away from keeping all powers in one person called Project Manager. All responsibilities were divided between the Development Team, the Scrum Master and the Product Owner. Trying to be both PO and SM would be re-creation of the Project Manager.
2) That would be a conflict of interest. From one side you're protecting a team (SM) and show their real capacity, from the
other side you want to get more and more features (PO) and business value. These are mutually exclusive directions.
3) The Scrum Master is a servant leader for the Team. This would be endangered if he/she becomes a PO


Hope that helps.

I'm now confronted with the need to replace an old tool by creating a more modern version of it. The end users (including me and 2 other colleagues) are the only one in the company to know the old tool, its history and the theory behind it. We are also the only one with programming skills. We would like to use Scrum to tackle the creation of the new tool. The problem is, we are only 3, and would all need to be part of the development team.

Hence the question: could 2 of us, as members of the development team, be endorsing the roles of SM & PO? Although it could be possible to train someone else in the company to become SM, the lack of knowledge in the old tool make it very hard to conceive having a different PO...

Thanks for the hints!

What does the Scrum Guide say about the size of a Development Team, and the circumstances under which the Scrum Master and Product Owner are included in the count?