**Authors:** Florentin Smarandache

We define a class of sequences {a_{n}} by a_{1} = a and a_{n+1} = P(a_{n}), where P is
a polynomial with real coefficients. For which a values, and for which polynomials P
will these sequences be constant after a certain rank? Then we generalize it from
polynomials P to real functions f.
In this note, the author answers this question using as reference F. Lazebnik & Y.
Pilipenko's E 3036 problem from A. M. M., Vol. 91, No. 2/1984, p. 140.
An interesting property of functions admitting fixed points is obtained.

**Comments:** 3 pages

**Download:** **PDF**

[v1] 13 Mar 2010

**Unique-IP document downloads:** 18 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *