Abstract
Let K be an algebraic number field of finite degree over the rationals. The bulk of the present paper is concerned with the problem about the occurrence of algebraic primes in irreducible polynomial sequences generated by polynomials of K with prime arguments from a residue class in K. We shall also deal with the problem of estimating the number of prime idealsT of K withT for which a given integer is a primitive root moduloT, improving on a result of Egami.
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