CARDINALITY OF SETS ASSOCIATED TO CERTAIN DEGREE SEVEN POLYNOMIALS - Lasaraiya, Suriana; Sapar, Siti Hasana; Mohamat Johari, Mohamat Aidil (Malaysian Journal of Science, 2015)
Let be a function of two variables. Let be an integer and let âˆ‘ , 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