一个二元二次同余方程解的计数  

Counting solutions of a binary quadratic congruence equation

作　　者：段然 DUAN Ran(School of Mathematics, Northwest University, Xi'an 710127, Shaanxi, China)

机构地区：[1]西北大学数学学院

出　　处：《山东大学学报（理学版）》2019年第8期108-120,共13页Journal of Shandong University(Natural Science)

摘　　要：设n是任意正整数,令Zn是模n的剩余类环,并且Z^*n是模n的即约剩余类环,即Z^*_n={s:1≤s≤n, gcd(s,n)=1}。通过利用同余理论与指数和的相关结果来研究集合T(a,b,c,n)={(x,y)∈(Z^*_n)^2:ax^2+by^2+c≡0 mod n}的元素个数并给出集合T(a,b,c,n)元素个数的确切计算公式。Let n be a positive integer. Denote by Z_n the ring of residue classes mod n, and by Z~*_n the group of units in Z_n, i.e. Z~*_n={s:1≤s≤n and gcd(s,n)=1}. The main purpose of this paper is using congruence conclusion and some results of exponential sums to study the number of elements of the set T(a,b,c,n)={(x,y)∈(Z~*_n)~2:ax^2+by^2+c≡0 mod n} and give an exact computational formula for the number of elements of T(a,b,c,n).

关 键 词：同余方程 剩余类环 指数和 集合划分 

分 类 号：O156.4[理学—数学]