Uniqueness of the Sum of Points of the Period-Five Cycle of Quadratic Polynomials

It is well known that the sum of points of the period-five cycle of the quadratic polynomial is generally not one-valued. In this paper we will show that the sum of cycle points of the curves of period five is at most three-valued on a new coordinate plane and that this result is essentially the best possible. The method of our proof relies on a implementing Gröbner-bases and especially extension theory from the theory of polynomial algebra.

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