论文信息 - Periodic solutions to some difference equations over the integers

Periodic solutions to some difference equations over the integers

In this paper, we investigate periodic integer solutions {a n } to where r is a rational number. We show that solutions can only exist, if − 1 ≤ r ≤ 1/2 and we give several infinite families of rs, for which the above recurrence has periodic solutions in the integers.

John R Greene | Katherine Niedzielski | John Greene | K. Niedzielski

[1] Carl D. Meyer,et al. Matrix Analysis and Applied Linear Algebra , 2000 .

[2] C. Kent,et al. On Some Difference Equations with Eventually Periodic Solutions , 1998 .

[3] J. H. E. Cohn,et al. On Square Fibonacci Numbers , 1964 .

[4] G. Ladas. Open problems and conjectures: Progress report on “difference equations with eventually periodic solutions” , 1997 .

[5] D. Clark,et al. Periodic solutions of arbitrary length in a simple integer iteration , 2006 .

[6] David Thomas,et al. The Art in Computer Programming , 2001 .

[7] B. E. Meserve. Fundamental Concepts of Algebra , 1982 .

[8] Jeffrey C. Lagarias,et al. The 3x + 1 Problem and its Generalizations , 1985 .

[9] G. Ladas,et al. A difference equation with eventually periodic solutions , 1998 .