Kvadratni ostatci i primjene

In this final paper we are going to introduce ourselves to quadratic residues and some of its applications. At the beginning, we will define quadratic residues and give some examples. In the first chapter, we will define Legendre’s symbol, enlist the basic properties of Legendre’s symbol and use those properties on an example. We will be, as well, introduced to Euler’s theorem. In the second chapter, we are going to express and prove Gauss’s lemma, quadratic law of reciprocity and we will show the usage of quadratic law of reciprocity. In the third chapter, we will define and introduce ourselves to the properties of Jacobi symbol and we’ll show the usage of the properties on an example. In the last chapter, we are going to express and prove some of applications of quadratic residues on Diophantine equations.