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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 575064, 9 pages
http://dx.doi.org/10.1155/2014/575064
Research Article

Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques

1Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
2Faculty of Information Technology, University of Central Punjab, Lahore 54500, Pakistan

Received 5 March 2014; Revised 6 April 2014; Accepted 10 April 2014; Published 5 May 2014

Academic Editor: Sher Afzal Khan

Copyright © 2014 M. Khalid Mahmood and Farooq Ahmad. 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

In this paper we put forward a family of algorithms for lifting solutions of a polynomial congruence to polynomial congruence . For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the form , where and are integers which are not divisible by an odd prime . It is shown that the algorithms suggested in this paper drastically reduce the complexity for such computations to a logarithmic scale. The efficacy of the proposed technique for solving negative exponent equations of the form has also been addressed.