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Positive rational number of the form $\varphi(km^{a})/\varphi(ln^{b})$
- Publication Year :
- 2022
-
Abstract
- 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.
- Subjects :
- Mathematics - Number Theory
11A25, 11D85
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2212.00918
- Document Type :
- Working Paper