Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498643 | Linear Algebra and its Applications | 2005 | 13 Pages |
Abstract
We show that a “periodic” version of the so-called conjecture of Collatz can be reformulated in terms of a determinantal identity for certain finite-dimensional matrices Mk, for all k ⩾ 2. Some results on this identity are presented. In particular we prove that if this version of the Collatz's conjecture is false then there exists a number k satisfying k â¡Â 8 (mod 18) for which the orbit of k2 is periodic.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
J.F. Alves, M.M. Graça, M.E. Sousa Dias, J. Sousa Ramos,