Abstract and Applied Analysis

Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques

M. Khalid Mahmood and Farooq Ahmad

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In this paper we put forward a family of algorithms for lifting solutions of a polynomial congruence m o d p to polynomial congruence m o d p k . For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the form a x n b ( m o d p k ) , k 1, where a , b, and n > 0 are integers which are not divisible by an odd prime p . 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 a x - n b ( m o d p k ) has also been addressed.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 575064, 9 pages.

First available in Project Euclid: 27 February 2015

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Mahmood, M. Khalid; Ahmad, Farooq. Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 575064, 9 pages. doi:10.1155/2014/575064. https://projecteuclid.org/euclid.aaa/1425049592

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