What just happened?

#1
  1. What do I need to study to be able to prove things like this?
  2. Are these modulus properties, that we should have known?
  3. If this concept can be studied can you recommend sources? I’m ready to read books if I have to. Even if they are math books.
#2

you can just follow the videos and that should be enough . you ll always find content you dont know .just keep revising them