تقرير
Positive rational number of the form $\varphi(km^{a})/\varphi(ln^{b})$
| العنوان: | Positive rational number of the form $\varphi(km^{a})/\varphi(ln^{b})$ |
|---|---|
| المؤلفون: | Li, Hongjian, Yuan, Pingzhi, Bai, Hairong |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11A25, 11D85 |
| الوصف: | Let $k, l, a$ and $b$ be positive integers with $\max\{a, \, b\}\ge2$. In this paper, we show that every positive rational number can be written as the form $\varphi(km^{a})/\varphi(ln^{b})$, where $m, \, n\in\mathbb{N}$ if and only if $\gcd(a, \,b)=1$ or $(a, b, k, l)=(2,2, 1, 1)$. Moreover, if $\gcd(a, b)>1$, then the proper representation of such representation is unique. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2212.00918 |
| رقم الأكسشن: | edsarx.2212.00918 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |