ABSTRACT
The main focus of this chapter is to introduce the solvability ofcongruence equations in one variable and systems of linear congruence equations and provide some concrete methods for finding their solutions. For a system of linear congruence equations, we will mainly discuss how to solve them using the Chinese remainder theorem. For general congruence equations, we describe a general process of finding solutions. For quadratic congruence equations, we consider the case of prime modulus, that is, the quadratic residue problem with prime modulus. Finally, we introduce an arithmetic function that is related to the quadratic residues, the Legendre symbol, and define a more general arithmetic function, the Jacobi symbol.
