JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 108-120.doi: 10.6040/j.issn.1671-9352.0.2018.407

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Counting solutions of a binary quadratic congruence equation

DUAN Ran   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: 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).

Key words: congruence equation, ring of residue class, exponential sum, set partition

CLC Number: 

  • O156.4
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