The Roots of Quadratic Equation and Cubic Equation Over F3n

Longsong Duan(1*), Delong Wan(2), Shengliang Zou(3)

(1) Gongqing College Nanchang University, China
(2) Gongqing College Nanchang University, China
(3) Gongqing College Nanchang University, China
(*) Corresponding author


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Abstract


In this paper, we give the formula of roots of the quadratic equations over finite field F3n according to the relation between the roots and coefficients, and the formula of roots of the cubic equations ax3 + cx + d = 0 over finite field F3n by trace function. We give the relationship between the part of the solutions and the coefficient of the equation z3 + z2 + α = 0.
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Keywords


Quadratic Equations, Cubic Equations, The Formula of Roots, Finite Field, Square Element

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