Topic
Nontotient
About: Nontotient is a research topic. Over the lifetime, 89 publications have been published within this topic receiving 614 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, it was shown that if n is a solution of (1), then n is either a prime or the product of seven or more distinct primes, and the proof of the nonexistence of composite solutions of this problem seems about as remote as the proof for the existence of odd perfect numbers.
Abstract: where k is an integer, and {n) is Euler's totient function, giving the number of integers (n) divides n — 1. We have not been able to establish this, however. The proof of the nonexistence of composite solutions of (1) seems about as remote as the proof of the nonexistence of odd perfect numbers and the two problems though not equivalent are not dissimilar. Let w b e a composite solution of (1) and let a be any number prime to n\\ then
85 citations
TL;DR: In this article, Menon's beautiful identity was extended to Dirichlet characters mod n, where the number of divisors is φ(n)τ(n).
Abstract: Let φ be the Euler’s totient function and τ(n) be the number of divisors of n. Menon’s beautiful identity states that ∑k=1gcd(k,n)=1ngcd(k−1,n) = φ(n)τ(n). Here we extend this identity to Dirichlet characters mod n.
35 citations
34 citations
TL;DR: The Jordan totient revisited: C. Jordan's generalization of the Euler o-function is disregarded in most textbooks on number theory and algebra today as discussed by the authors, but it has been used extensively in finite group theory and complex representation theory.
Abstract: The Jordan totient revisited: C. Jordan’s generalization of the Euler o—function is disregarded in most textbooks on number theory and algebra today. We prove some results about this important arithmetical function and demonstrate its usage in finite group theory and complex representation theory. Our interest in this totient was “induced” by studying all complex representations of finite nilpotent Heisenberg groups. The structure of the dual of these groups can be related to a theorem on Jordan totients. Our theorems lead to some peculiar equations involving the greatest common divisor (in German: ggT).
18 citations
TL;DR: The main goal of as discussed by the authors is to provide a group theoretical generalization of the well-known Euler's totient function, which determines an interesting class of finite groups, namely, Euler groups.
Abstract: The main goal of this paper is to provide a group theoretical generalization of the well-known Euler’s totient function. This determines an interesting class of finite groups.
15 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 3 |
| 2016 | 5 |
| 2015 | 8 |
| 2014 | 5 |
| 2013 | 8 |
| 2012 | 5 |