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On The Estimate to Solutions of Congruence Equations Associated with a Quartic form


Chan, Kait Loon (1997) On The Estimate to Solutions of Congruence Equations Associated with a Quartic form. Masters thesis, Universiti Putra Malaysia.


The set of solutions to congruence equations modulo a prime power associated with the polynomial in Zp[x,y] is examined and its cardinality is estimated by employing the Newton polyhedral technique.The method involves reduction of the partial derivatives of f that is f" and fy into polynomials with single variable and finding 8 the determinant factor in the estimation. fx and fy are reduced to one-variable polynomials by employment of suitable parameters. The Newton polyhedrons associated with the polynomials so obtained are then considered and combination of their Indicator diagrams examined. There exist common zeros of the single- variable polynomials whose p-adic orders correspond to the intersection points in the combination of the Indicator diagrams associated with the respective Newton polyhedrons of the polynomials. The p-adic sizes of these zeros are then determined, and this leads to sizes of common zeros of the partial derivatives of f. This information is then used to arrive at the estimate of the cardinality above.

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Additional Metadata

Item Type: Thesis (Masters)
Subject: Congruences and residues
Call Number: FSAS 1997 6
Chairman Supervisor: Professor Dr. Kamel Ariffin bin Mohd. Atan
Divisions: Faculty of Environmental Studies
Depositing User: Nurul Hayatie Hashim
Date Deposited: 03 Dec 2010 09:05
Last Modified: 08 May 2012 07:14
URI: http://psasir.upm.edu.my/id/eprint/8621
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