### The Roots of Quadratic Equation and Cubic Equation Over F3n

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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. *Copyright © 2014 Praise Worthy Prize - All rights reserved.*

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