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arXiv · 2502.18252

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

Weilin Zhang·Fengyuan Chen·Hongjian Li·Pingzhi Yuan
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Abstract

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 $\varphi(m^{2})/(\varphi(n^{2}))^{b}$ and $\varphi(k(m^{2}-1))/\varphi(ln^{2})$, where $m, n\in \mathbb{N}$ and $\varphi$ is the Euler's totient function. At the end, some further results are discussed.

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Weilin Zhang, Fengyuan Chen, Hongjian Li, Pingzhi Yuan. 2025-02-25. On the representation of rational numbers via Euler's totient function. https://arxiv.org/abs/2502.18252

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