If $p$ and $q$ are positive irrationals such that $$\frac{1}{p}+\frac{1}{q}=1$$ then the sequences \begin{eqnarray*} \{\lfloor np\rfloor\}_{n=1}^\infty&=&\lfloor p\rfloor,\lfloor 2p\rfloor,\lfloor 3p\rfloor,\ldots\\ \{\lfloor nq\rfloor\}_{n=1}^\infty&=&\lfloor q\rfloor,\lfloor 2q\rfloor,\lfloor 3q\rfloor,\ldots\\ \end{eqnarray*}where $\lfloor x\rfloor$ denotes the floor (or greatest integer function) of $x$ constitute a partition of the set of positive integers.

That is, every positive integer is a member exactly once of one of the two sequences and the two sequences have no common terms.