That's actually really cool!

Algebra Level 5

α,2α,3α, and β,2β,3β,\lfloor \alpha \rfloor,\lfloor 2\alpha \rfloor, \lfloor 3\alpha \rfloor, \ldots \quad \text{ and } \quad \lfloor \beta \rfloor, \lfloor 2\beta \rfloor,\lfloor 3\beta \rfloor, \ldots

Let α\alpha and β\beta be positive irrational numbers such that the sequences above contain every positive integer exactly once. i.e. If you pick a positive integer, it will appear in only one of the above sequences. Which of the following statements are true?

Notation: \lfloor \cdot \rfloor denotes the floor function.

×

Problem Loading...

Note Loading...

Set Loading...