**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.

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[v1] 13 Mar 2010

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