| Автор | Berenhaut, Kenneth S. |
| Автор | Stancil, Bennett J. |
| Автор | Newman, Jonathan H. |
| Дата выпуска | 2009 |
| dc.description | This paper studies solutions of some piecewise-linear difference equations. In two particular cases, a descent argument is used to show that all solutions are periodic with either prime period 3(2<sup> k </sup> − 1) or 6(2<sup> k </sup> − 1) for some k ≥ 1. The existence of solutions with such periods is also considered. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | piecewise-linear difference equation |
| Тема | periodicity |
| Тема | descent |
| Тема | recursive equation |
| Тема | Mersenne numbers |
| Тема | 39A10 |
| Тема | 39A11 |
| Название | A note on some piecewise-linear difference equations with Mersenne-type periodic solutions |
| Тип | research-article |
| DOI | 10.1080/10236190802271449 |
| Electronic ISSN | 1563-5120 |
| Print ISSN | 1023-6198 |
| Журнал | Journal of Difference Equations and Applications |
| Том | 15 |
| Первая страница | 729 |
| Последняя страница | 733 |
| Аффилиация | Berenhaut, Kenneth S.; Department of Mathematics, Wake Forest University |
| Аффилиация | Stancil, Bennett J.; Department of Mathematics, Wake Forest University |
| Аффилиация | Newman, Jonathan H.; Department of Mathematics, Wake Forest University |
| Выпуск | 7 |
| Библиографическая ссылка | Amleh, A.M., Grove, E.A., Kent, C.M. and Ladas, G. 1998. On some difference equations with eventually periodic solutions. J. Math. Anal. Appl., 223: 196–215. |
| Библиографическая ссылка | Clark, D. and Lewis, J. 1995. A Collatz-type difference equation. Congr. Numer., 3: 129–135. |
| Библиографическая ссылка | Feuer, J. 2004. Two classes of piecewise-linear difference equations with eventual periodicity six. J. Math. Anal. Appl., 295(2): 570–575. |
| Библиографическая ссылка | Feuer, J. 2007. Two classes of piecewise-linear difference equations with eventual periodicity three. J. Math. Anal. Appl., 332(1): 564–569. |
| Библиографическая ссылка | Feuer, J. and Ladas, G. 2004. Open problems and conjectures. J. Difference Equ. Appl., 10: 447–451. |
| Библиографическая ссылка | Lagarias, J.C. 1985. Amer. Math. Monthly, 92: 3–21. The 3x+1 problem and its generalizations |
| Библиографическая ссылка | Wirsching, G.J. 2000. Elem. Math., 55(4): 142–155. Über das 3n+1 problem |
