Carmichael meets chebotarev

摘要

For any finite Galois extension K of Q and any conjugacy class C in Gal(K=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 ε Z.