Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1888391 | Chaos, Solitons & Fractals | 2016 | 4 Pages |
Abstract
Let (Gm)m ≥ 0 be an integer linear recurrence sequence (under some weak technical conditions) and let x ≥ 1 be an integer. In this paper, we are interested in the problem of finding combinations of the form xGn+Gn−1xGn+Gn−1 which belongs to (Gm)m ≥ 0 for infinitely many positive integers n. In this case, we shall make explicit an upper bound for x which only depends on the roots of the characteristic polynomial of this recurrence. As application, we shall study the k-nacci case.
Keywords
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Pavel Trojovský,