AN EXTENSION OF THE THEOREM ON PRIMITIVE DIVISORS IN ALGEBRAIC NUMBER-FIELDS

The theorem about primitive divisors in algebraic number fields is gen eralized in the following manner. Let A, B be algebraic integers, (A, B) = 1, AB not-equal 0, A/B not a root of unity, and zeta(k) a primiti ve root of unity of order k . For all sufficiently large n, the number A(n) - zeta(k)B(n) has a prime ideal factor that does not divide A(m) - zeta(k)j(B)(m) for arbitrary m < n and j < k.