Πρώτοι Αριθμοί

• Main Authors: Πουλάκης, Δημήτριος, Poulakis, Dimitrios
• Format: 7
• Language: Greek
• Published: 2016
• Subjects: ΥΠΟΛΟΓΙΣΤΙΚΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ; ΙΣΟΤΙΜΙΕΣ; ΓΡΑΜΜΙΚΕΣ ΙΣΟΤΙΜΙΕΣ; ΤΕΤΡΑΓΩΝΙΚΑ ΥΠΟΛΟΙΠΑ; ΠΕΠΕΡΑΣΜΕΝΑ ΣΩΜΑΤΑ; Computational Number Theory; Congruences; Linear Congruences; Quadratic Residues; Finite Fields

Chapter 4 is devoted to the congruence relations of integers, the description of the properties of their classes and the running time of the execution of theirs basic operations. We study the resolution of linear congruences and theirs systems and we determine for which positive integers there are primitive roots modulo n. Furthermore, we introduce Legendre and Jacobi symbols and we present algorithms for the computation of Jacobi symbols and the solution of quadratic congruences. Finally, we introduce the notion of congruence between polynomials and we give the constuction of finite fields and some basic properties.