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Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques

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  • M. Khalid Mahmood
  • Farooq Ahmad

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.

Suggested Citation

  • M. Khalid Mahmood & Farooq Ahmad, 2014. "Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, May.
    • Handle: RePEc:hin:jnlaaa:575064
    DOI: 10.1155/2014/575064
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