A NOTE ON CARMICHAEL'S CONJECTURE
Antonio A. Andrade1, Guilherme Z. Cundari2
1,2 Department of Mathematics
São Paulo State University
São José do Rio Preto - SP, 15054-000, BRAZIL

Abstract

Euler's totient function (also known as Euler's $\varphi$-function or just Euler's function) was introduced by Leonhard Euler (1707-1783) in 1760, motivated by a problem proposed by Pierre of Fermat (1607-1665). Given a positive integer $n$, in this work, we present new results about the existence of a positive integer $m$ such that $\varphi(m) = \varphi(n)$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 3
Year: 2022

DOI: 10.12732/ijam.v35i3.3

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References

  1. [1] P. Ribenboim, The Little Book of Bigger Primes, Springer Verlag, New York (1991).
  2. [2] R.D. Carmichael, Note on Euler’s '-function, Bull. Amer. Math. Soc., 28 (1922), 109-110.