%A DUAN Ran
%T Counting solutions of a binary quadratic congruence equation
%0 Journal Article
%D 2019
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2018.407
%P 108-120
%V 54
%N 8
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3137.shtml}
%8 2019-08-20
%X Let n be a positive integer. Denote by Zn the ring of residue classes mod n, and by Z*n the group of units in Zn, 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:ax2+by2+c≡0 mod n} and give an exact computational formula for the number of elements of T(a,b,c,n).