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A note on some piecewise-linear difference equations with Mersenne-type periodic solutions |
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| Authors: | Kenneth S. Berenhaut Bennett J. Stancil Jonathan H. Newman |
| Affiliation: | 1. Department of Mathematics , Wake Forest University , Winston-Salem, NC, USA berenhks@wfu.edu;3. Department of Mathematics , Wake Forest University , Winston-Salem, NC, USA |
| Abstract: | 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 k ? 1) or 6(2 k ? 1) for some k ≥ 1. The existence of solutions with such periods is also considered. |
| Keywords: | piecewise-linear difference equation periodicity descent recursive equation Mersenne numbers |