I am stuck with these two floor function problems.
Please help me
1. Let r be a real number, and n be a positive integer.
2. Let S be set of integers given by $[\alpha x]$ and $[\beta x]$ for x=1,2,3,...
Prove that S consists of every integer, each appearing exactly once, iff $\alpha$ and $\beta$ are positive irrational numbers such that $\frac1\alpha+\frac1\beta=1$