Recursive Elucidation of Polynomial Congruences Using Root‐Finding Numerical Techniques

M. Khalid Mahmood and Farooq Ahmad

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: In this paper we put forward a family of algorithms for lifting solutions of a polynomial congruence mod p to polynomial congruence mod pk. For this purpose, root‐finding iterative methods are employed for solving polynomial congruences of the form axn ≡ b(mod pk), 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 ax−n ≡ b(mod pk) has also been addressed.

Date: 2014
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https://doi.org/10.1155/2014/575064

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:575064

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