On quadratic reciprocity law

• Main Authors: Salud, Cristina R., Sumang, Marie Christine P.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Numbers, Theory of; Quadratic; Congruences (Geometry); Reciprocity theorems
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16173
• Institution: De La Salle University

This thesis discusses quadratic congruences and Gauss' Quadratic Reciprocity Law. Quadratic congruences of the form ax2 + bx + c = 0(mod p), where p is an odd prime and a = 0 (mod p), may or may not have solutions. If they are solvable, the only way to obtain the roots is to substitute a complete residue system modulo p. For large p, doing this would be tedious and would be disappointing if, after inspecting a complete residue system of p, one finds out that no solution exists. Thus it is important to know the methods of determining the solvability of a given quadratic congruence. Some of such methods, of which the Quadratic Reciprocity Law is the most important, are presented in this paper.