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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 893045, 10 pages
http://dx.doi.org/10.1155/2013/893045
Research Article

A Non-NP-Complete Algorithm for a Quasi-Fixed Polynomial Problem

1Department of General Education, National Army Academy, Taoyuan 320, Taiwan
2Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan

Received 15 January 2013; Accepted 24 February 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 Yi-Chou Chen and Hang-Chin Lai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a real-valued polynomial function of the form , with degree of in An irreducible real-valued polynomial function and a nonnegative integer are given to find a polynomial function satisfying the following expression: for some constant . The constant is dependent on the solution , namely, a quasi-fixed (polynomial) solution of the polynomial-like equation . In this paper, we will provide a non-NP-complete algorithm to solve all quasi-fixed solutions if the equation has only a finite number of quasi-fixed solutions.