On the representation of rational numbers via Euler's totient function

Let $b>1$ be an odd positive integer and $k,l\in \mathbb{N}$. In this paper, we show that every positive rational number can be written as $\phi (m^2)\mathrm{/}(\phi (n^2){)}^b$ and $\phi (k(m^2-1))\mathrm{/}\phi (l{n}^2)$, where $m,n\in \mathbb{N}$ and $\phi$ is the Euler’s totient function. At the end, some further results are discussed.