CARDINALITY OF SETS ASSOCIATED TO CERTAIN DEGREE SEVEN POLYNOMIALS

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Suriana Lasaraiya
Siti Hasana Sapar
Mohamat Aidil Mohamat Johari

Abstract

Let be a function of two variables. Let be an integer and let ∑ , where the sum is taken over a complete set of residue modulo . The value of depends on the estimate of the cardinality of the following set { where and are the partial derivative of with respect to and . In this paper, we discuss the cardinality, of the set of solutions for congruence equations of some special binary forms. Firstly we need to obtain the p-adic sizes of common zeros of the partial derivative polynomials by using Newton polyhedron technique. The polynomial that we consider is in the form of .


Keywords: -adic order, Newton Polyhedron, Indicator diagram, Cardinality

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