Hello!

I have a test this week and some examples where I have no idea! These are some bonus problems, but I want to solve them.

The problem is:

Do there exist real numbers a,b,c such that Spec(a), Spec(b), Spec(c) together partition the set of positive integers?

Spec....spectrum of a real number

Its defined as: Spec(a)={[a],[2a],.....}BUT [ ] means the greatest integer less than or equal to a. - (the Gauss brackets)

I hope someone can help me