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- 2015
有限域上某些方程的解数公式
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Abstract:
摘要 给出有限域Fq(q=ps, s≥1, p是一个奇素数)上的方程 x1m1+…+xnmn=cx1…xt 和 (x1+…+xn)2=cx1…xt 在一定条件下的解数公式, 其中mj|q-1,n≥2,c∈Fq*,t > n.当m1=…=mn=m时, 给出了方程x1m+…+xnm=cx1…xt的解数的显示公式.
| [1] | Baulina Y N. On explicit formulas for the number of solutions to the equation(x<sub>1</sub>+…+x<sub>n</sub>)<sup>2</sup>=ax<sub>1</sub>…x<sub>n</sub> in a finite field[J]. Siberian Mathematical Journal, 2003, 1:17-21. |
| [2] | Small C. Arithmetic of finite fields[M]. New York:Marcel Dekker, 1991. |
| [3] | Baoulina I. On the number of solutions to certain diagonal equations over finite fields[J]. International Journal of Number Theory, 2010, 1:1-14.</p> |
| [4] | Sun Q, Wan D Q. On the solvability of the equation ???x<sub>i</sub>/d<sub>i</sub>≡0 (mod 1) and its application[J]. Proceedings of The American Mathematical Society, 1987, 100:220-224. |
| [5] | Sun Q, Wan D Q. On the diophantine equation ???x<sub>i</sub>/d<sub>i</sub>≡0 (mod 1)[J]. Proceedings of the American Mathematical Society, 1991, 112:25-29. |
| [6] | Sun Q, Wan D Q, Ma D G. On the diophantine equation ???x<sub>i</sub>/d<sub>i</sub>≡0 (mod 1) and its applications[J]. Chinese Annals of Mathematics Series B, 1986, 7:232-236. |
| [7] | Baoulina I. On the equation(x<sub>1</sub><sup>m<sub>1</sub></sup>+…+x<sub>n</sub><sup>m<sub>n</sub></sup>)<sup>k</sup>=ax<sub>1</sub>…x<sub>n</sub> over a finite field[J]. International Journal of Number Theory, 2006, 2:351-363. |
| [8] | Zhao Z J, Cao X W. On the number of solutions of certain equations over finite fields[J]. Journal of Mathematical Research & Exposition, 2010, 3:957-966. |
| [9] | Baoulina I. On the problem of explicit evaluation of the number of solutions of equation a<sub>1</sub>x<sub>1</sub><sup>2</sup>+…+a<sub>n</sub>x<sub>n</sub><sup>2</sup>=bx<sub>1</sub>…x<sub>n</sub> in a finite field[C]//Adhikari S D, Katre S A, Ramakrishnan B. Current Trends in Number Theory. New Delhi:Hindustan Book Agency, 2002:27-37. |
| [10] | Luo Y M, Zhao Z J, Cao X W. On the number of solutions of the equation a<sub>1</sub>x<sub>1</sub><sup>2</sup>+…+a<sub>n</sub>x<sub>n</sub><sup>2</sup>=bx<sub>1</sub>…x<sub>s</sub> in finite fields[J]. International Journal of Pure and Applied Mathematics, 2009, 4:569-576. |
| [11] | Cao W, Sun Q. Factorization formulae on counting zeros of diagonal equations over finite fields[J]. Proceedings of the American Mathematical Society, 2007, 135:1283-1291. |
| [12] | Baoulina I. On systems of linear and diagonal equations of degreep<sup>i</sup>+1 over finite fields of characteristic p[J]. Finite Fields and Their Applications, 2008, 14:648-657. |
| [13] | <p> Carlitz L. Certain special equations in a finite field[J]. Monatshefte Für Mathematik, 1954, 58:5-12. |
| [14] | Baoulina I. On the equation x<sub>1</sub><sup>m<sub>1</sub></sup>+…+x<sub>n</sub><sup>m<sub>n</sub></sup>=ax<sub>1</sub>…x<sub>n</sub> over a finite field[J]. Finite Fields and Their Applications, 2007, 13:887-895. |
| [15] | Baoulina I. On the number of solutions of the equation a<sub>1</sub>x<sub>1</sub><sup>m<sub>1</sub></sup>+…+a<sub>n</sub>x<sub>n</sub><sup>m<sub>n</sub></sup>=bx<sub>1</sub>…x<sub>n</sub> in a finite field[J]. Acta Applicandae Mathematica, 2005, 89:35-39. |
| [16] | Baoulina I. On some equations over finite fields[J]. Journal de Theorie des Nombres de Bordeaux, 2005, 17:45-50. |
| [17] | Baoulina I. Generalizations of the Markoff-Hurwitz equations over finite fields[J]. Journal of Number Theory, 2006, 118:31-52. |
