Application of the p-Adic Topology on ℤ to the Problem of Finding Solutions in Integers of an Implicit Linear Difference Equation
Journal Article
·
· Journal of Mathematical Sciences
- Karazin Kharkiv National University (Ukraine)
We study solutions in integers of an implicit linear inhomogeneous first order difference equation bx{sub n+1} = ax{sub n} + f{sub n}. Based on the p-adic topology on the ring of integers, we obtain a criterion for the existence of solutions and show that for a = 1 a typical (in the natural topological sense) equation has no integer solutions.
- OSTI ID:
- 22773684
- Journal Information:
- Journal of Mathematical Sciences, Vol. 235, Issue 3; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 1072-3374
- Country of Publication:
- United States
- Language:
- English
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