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有限域上对角方程axd+by2d=c的可解性

2023-04-29陈燎强诗瑗陈龙

关键词:荣军解性陈龙

陈燎 强诗瑗 陈龙

收稿日期: 2023-04-12

基金项目: 攀枝花学院2022年校级科研项目(攀学院[2022]65号-13); 太阳能技术集成及应用推广四川省高校重点实验室项目(TYNSYS-2022-C-02)

作者简介: 陈燎(1997- ), 男, 四川巴中人, 硕士研究生, 主要研究方向为数论及其应用. E-mail: chenliao1@stu.scu.edu.cn

通讯作者: 陈龙. E-mail: chenlongscumath@126.com

参考文献:

[1]Lidl R, Niederreiter H. Finite fields [M]. Cambridge: Cambridge University Press, 1997.

[2]黄宝盛, 吴荣军, 谭千蓉, 等. 有限域上四次对角方程 ax4+by4=c解的存在性[J]. 四川大学学报: 自然科学版, 2022, 59: 011001.

[3]孙琦. 有限域上某些对角方程的解数[J]. 四川大学学报: 自然科学版, 1997, 34: 395.

[4]Bergelson V, Best A, Iosevich A. Sums of powers in large finite fields: a mix of methods [J].  Amer Math Monthly, 2021, 128: 701.

[5]Chowla S, Cowles J, Cowles M. On the number of zeros of diagonal cubic forms [J]. J Number Theory, 1977, 9: 502.

[6]Dickson L E. On the congruencexn+yn+zn≡0mod p [J]. J Rein Angew Math, 1909, 135: 134.

[7]Hong S F, Zhu C X. On the number of zeros of diagonal cubic forms over finite fields [J]. Forum Math, 2021, 33: 697.

[8]Lagrange J L. Démonstration d′un théorème d′aritbmétique [J]. Mémoires Acad Roy Oeuvres,1770, 3: 189.

[9]Myerson G, On the number of zeros of diagonal cubic forms [J]. J Number Theory, 1979, 11: 95.

[10]Singh S. Analysis of each integer as sum of two cubes in a finite integral domain [J]. Indian J Pure Appl Math, 1975, 1: 29.

[11]Skolem T,S?tze Z, ?berdie K [J]. Norske Vid Selsk Forh, 1937, 10: 89.

[12]Small C. Sums of powers in large finite fields [J]. Proc Amer Math Soc, 1977, 65: 35.

[13]Zhao J, Feng Y, Hong S, et al. On the number of zeros of diagonal quartic forms over finite fields [J]. Forum Math. 2022, 34: 385.

[14]Hurwitz A,?ber die K. axe+bye+cze≡0mod p[J]. J Rein Angew Math, 1909, 136: 272.

[15]Ahlfors L. Complex analysis [M]. New York: McGraw-Hill, 1979.

引用本文格式:

中 文: 陈燎, 强诗瑗, 陈龙. 有限域上对角方程axd+by2d=c的可解性[J]. 四川大学学报: 自然科学版, 2023, 60: 061003.

英 文: Chen L, Qiang S Y, Chen L. Solvability of diagonal equation axd+by2d=c over finite fields [J]. J Sichuan Univ: Nat Sci Ed, 2023, 60: 061003.

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