English

On Carmichael's Conjecture

General Mathematics 2007-05-23 v1

Abstract

In this article we prove that equation ϕ(x)=n\phi(x)=n, for a fixed nn, admits a finite number of solutions, we find the general form of these solutions, and we show that: if x0x_0 is a unique solution of this equation then x0x_0 is a product of a very large number of primes (we conjecture that the number of such primes is infinite).

Keywords

Cite

@article{arxiv.0704.2453,
  title  = {On Carmichael's Conjecture},
  author = {Florentin Smarandache},
  journal= {arXiv preprint arXiv:0704.2453},
  year   = {2007}
}
R2 v1 2026-06-21T08:20:01.875Z