Question 48
Let the numbers $r, s \in [1, \infty)$ with the property that for every positive integers $a, b$, with $a$ dividing $b$, it results that $[ar]$ divides $[bs]$.
a) Prove that $\frac{s}{r}$ is a positive integer.
b) Show that $r$ and $s$ are positive integers.
*Remark.* By $[x]$ we denote the floor of the real number $x$.
a) Prove that $\frac{s}{r}$ is a positive integer.
b) Show that $r$ and $s$ are positive integers.
*Remark.* By $[x]$ we denote the floor of the real number $x$.