Geodesic
Carmichael Meets Chebotarev
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 695-708

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DOI

For any finite Galois extension $K$ of $\mathbb{Q}$ and any conjugacy class $C$ in $\text{Gal}\left( {K}/{\mathbb{Q}}\; \right)$ , 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 ${{a}^{2}}\,+\,n{{b}^{2}}$ with $a,\,b\,\in \,\mathbb{Z}$ .
DOI : 10.4153/CMB-2012-034-x
Mots-clés : 11N25, 11R45, Carmichael numbers, Chebotarev density theorem 
Banks, William D.; Güloğlu, Ahmet M.; Yeager, Aaron M. Carmichael Meets Chebotarev. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 695-708. doi: 10.4153/CMB-2012-034-x
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     author = {Banks, William D. and G\"ulo\u{g}lu, Ahmet M. and Yeager, Aaron M.},
     title = {Carmichael {Meets} {Chebotarev}},
     journal = {Canadian mathematical bulletin},
     pages = {695--708},
     year = {2013},
     volume = {56},
     number = {4},
     doi = {10.4153/CMB-2012-034-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-034-x/}
}
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