Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# Carmichael meets Chebotarev

Published:2012-09-21
Printed: Dec 2013
• William D. Banks,
Department of Mathematics, University of Missouri, Columbia, MO 65211 USA
• Ahmet M. Güloğlu,
Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, TURKEY
• Aaron M. Yeager,
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
 Format: LaTeX MathJax PDF

## Abstract

For any finite Galois extension $K$ of $\mathbb Q$ and any conjugacy class $C$ in $\operatorname {Gal}(K/\mathbb Q)$, we show that there exist infinitely many Carmichael numbers composed solely of primes for which the associated class of Frobenius automorphisms is $C$. This result implies that for every natural number $n$ there are infinitely many Carmichael numbers of the form $a^2+nb^2$ with $a,b\in\mathbb Z$.
 Keywords: Carmichael numbers, Chebotarev density theorem
 MSC Classifications: 11N25 - Distribution of integers with specified multiplicative constraints 11R45 - Density theorems

© Canadian Mathematical Society, 2014 : https://cms.math.ca/