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1. CMB 2012 (vol 56 pp. 695)

Banks, William D.; Güloğlu, Ahmet M.; Yeager, Aaron M.
 Carmichael meets Chebotarev 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 theoremCategories:11N25, 11R45
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