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模素数p下整数0的二次分拆的计数

Counting quadratic partitions of integer zero modulo prime numberp
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摘要 利用解析的方法以及一类模素数p的特征和的性质,研究了当p≡5(mod 6)时同余方程x_(1)^(2)+x_(2)^(2)+x_(3)^(2)+x_(4)^(2)≡0(mod p)解的个数,给出精确的计算公式。同时,研究了由4个元素所组成的模p下整数0的分拆,其中分拆中的元素均取自模p的二次剩余,将整数0的分拆共分为3类,并对每一类分拆的个数给出了精确的计算公式。 The main purpose of this research is using the analytic method and properties of a kind of Dirichlet character sum modulo p with p≡5(mod 6)to study the number of solutions of congruence equation x_(1)^(2)+x_(2)^(2)+x_(3)^(2)+x_(4)^(2)≡0(mod p).The accurate calculation formulas were given.Also,it is proved that the four-part partitions of 0 with all four parts chosen from the set of non-zero quadratic residues mod p.Such partitions are divided into three types.The exact calculation formula for the number of partitions of each type is given.
作者 王啸 邵凡晖 WANG Xiao;SHAO Fanhui(School of Science,Chang’an University,Xi’an 710064,China)
机构地区 长安大学理学院
出处 《纺织高校基础科学学报》 CAS 2023年第3期92-97,共6页 Basic Sciences Journal of Textile Universities
基金 陕西省自然科学基础研究计划项目(2022JQ-058)。
关键词 Dirichlet特征和 同余方程 整数分拆 计算公式 Dirichlet character sum congruence equation integer partition calculation formulas
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