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.
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Keywords


Quadratic Equations; Cubic Equations; the Ormula of Roots; Finite Field; Square Element

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References


J. V. Leyendekkers, A. G. Shannon, Analysis of the roots of some Cardano cubics, Notes Number Theory Discrete Math. Vol. 6 n. 4, 2000, pp. 113-117.

H. K. Pathak, A. S. Grewal, Geometrical solution of some cubic equations with non-real roots, Internat. J. Math. Ed. Sci. Tech. vol.33, n. 4, 2002, pp.575--596.

L. Euler, A Conjecture on the forms of the roots of equations, arXiv:math/0606194 [math.CV]

Q. J. Wang, The history of the formula for the roots of a cubic equation, Collected research papers on the history of mathematics, vol. 3, 1992, pp.148--151.

Z.M. Sun, The roots of cubic equations over the 2 k-element field. Journal of Inner Mongolia Normal University(Natural Science Edition),n. 2, 1993, pp.21--26.

V.I. Lebedev, On formulae for roots of cubic equation, Soviet Journal of Numerical Analysis and Mathematical Modelling, vol. 6, n. 4, 1991, pp. 315--324.
http://dx.doi.org/10.1515/rnam.1991.6.4.315

R. Lidl, G. L. Mullen, When does a polynomial over a finite field permute the elements of the field? Amer. Math. Monthly, vol.95, n. 3, 1988, pp. 243-246.
http://dx.doi.org/10.2307/2323626

C. Chen, Formulas for the solutions of quadratic equations over, IEEE Trans. Inform. Theory, vol. 28, 1982, pp.792-794.
http://dx.doi.org/10.1109/tit.1982.1056557

C. Wayne Walker, New Formulas for Solving Quadratic Equations over Certain Finite Field, IEEE Trans. Inform. Theory, vol. 45,n.1, 1982, pp. 782-794.
http://dx.doi.org/10.1109/18.746816

Z.M. Sun, The Roots of the Cubic Equations F2m Over a Field F3k, Journal of Guangxi Teachers College(Natural scienEdition), n.2,1995, pp.32-34.

Z.M. Sun, The Roots of the Cubic Equations over Field F2k, Jourrnal of Inuer Mongolia Normal University(Natural scien Edition), n. 2, 1993, pp. 21-26.

Z.M. Sun, The formula of roots of a quadratic equation over a field F2k, Mathematics in Practice and Theory, vol. 31, n.6, 2001, pp. 732-733.

Z.M. Sun, Quadratic Equations and Cubic Equations over a Field Fpk, Journal of Taishan University, vol. 33, n. 3, 2011, pp. 8-15.

C. Ding, Q. Xiang, J. Yuan, P. Yuan, Explicit classes of permutation polynomials of F33m, Sci. China Ser. A, vol. 52, n. 4, 2009, pp.639–647.
http://dx.doi.org/10.1007/s11425-008-0142-8


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