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Coincidences in generalized Lucas sequences
For an integer , let be the generalized
Lucas sequence which starts with ( terms) and each term
afterwards is the sum of the preceding terms. In this paper, we find all
the integers that appear in different generalized Lucas sequences; i.e., we
study the Diophantine equation in nonnegative integers
with . The proof of our main theorem uses lower
bounds for linear forms in logarithms of algebraic numbers and a version of the
Baker-Davenport reduction method. This paper is a continuation of the earlier
work [4].Comment: 14 page
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