## Quadratic Congruences## Introduction
Quadratic congruences are of the form \( x^2\equiv a \) (mod \( n \)). Some of them have, and some of them don’t have solutions. The In this article we discuss basic and advanced properties of these symbols and show how the theory of quadratic residues is applied in Diophantine equations and other types of problems that can hardly be solved otherwise. No knowledge on advanced number theory is presumed. ## Table of ContentsQuadratic congruences to prime moduliQuadratic congruences to composite moduli Some sums of Legendre’s symbols Problems |

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