An extension of the theorem on primitive divisors in algebraic number fields

Author:
A. Schinzel

Journal:
Math. Comp. **61** (1993), 441-444

MSC:
Primary 11R47; Secondary 11R04

MathSciNet review:
1189523

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Abstract: The theorem about primitive divisors in algebraic number fields is generalized in the following manner. Let *A, B* be algebraic integers, , *A/B* not a root of unity, and a primitive root of unity of order *k*. For all sufficiently large *n*, the number has a prime ideal factor that does not divide for arbitrary and .

**[1]**J. Browkin,*𝐾-theory, cyclotomic equations, and Clausen’s function*, Structural properties of polylogarithms, Math. Surveys Monogr., vol. 37, Amer. Math. Soc., Providence, RI, 1991, pp. 233–273. MR**1148382**, 10.1090/surv/037/11**[2]**E. Dobrowolski,*On a question of Lehmer and the number of irreducible factors of a polynomial*, Acta Arith.**34**(1979), no. 4, 391–401. MR**543210****[3]**A. Schinzel,*Primitive divisors of the expression 𝐴ⁿ-𝐵ⁿ in algebraic number fields*, J. Reine Angew. Math.**268/269**(1974), 27–33. Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, II. MR**0344221**

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1189523-2

Article copyright:
© Copyright 1993
American Mathematical Society