Number Theory and Applications

• Κύριοι συγγραφείς: Αντωνιάδης, Ιωάννης, Κοντογεώργης, Αριστείδης, Antoniadis, Ioannis, Kontogeorgis, Aristeidis
• Μορφή: 1
• Γλώσσα: Greek
• Έκδοση: 2015
• Θέματα: ΔΙΟΦΑΝΤΙΚΕΣ ΕΞΙΣΩΣΕΙΣ; ΙΣΟΤΙΜΙΕΣ; ΤΕΤΡΑΓΩΝΙΚΑ ΥΠΟΛΟΙΠΑ; ΝΟΜΟΣ ΤΕΤΡΑΓΩΝΙΚΗΣ ΑΝΤΙΣΤΡΟΦΗΣ; ΑΡΧΙΚΕΣ ΡΙΖΕΣ; ΔΕΙΚΤΕΣ; ΤΕΣΤ ΕΛΕΓΧΟΥ ΠΡΩΤΩΝ ΑΡΙΘΜΩΝ; ΠΑΡΑΓΟΝΤΟΠΟΙΗΣΗ; ΚΡΥΠΤΟΓΡΑΦΙΑ; ΣΥΝΕΧΗ ΚΛΑΣΜΑΤΑ; ΕΞΙΣΩΣΗ ΤΟΥ ΠΕΛΛ; ΤΕΤΡΑΓΩΝΙΚΕΣ ΜΟΡΦΕΣ; ΤΕΤΡΑΓΩΝΙΚΑ ΣΩΜΑΤΑ ΑΡΙΘΜΩΝ; ΚΩΔΙΚΟΠΟΙΗΣΗ; ΒΑΣΗ ΑΚΕΡΑΙΟΤΗΤΑΣ; ΔΙΑΚΡΙΝΟΥΣΑ; ΘΕΜΕΛΙΩΔΗΣ ΜΟΝΑΔΑ; ΝΟΜΟΣ ΑΝΑΛΥΣΗΣ; ΑΡΙΘΜΟΣ ΚΛΑΣΕΩΝ ΙΔΕΩΔΩΝ; ΦΙΜΠΟΝΑΤΣΙ ΚΑΙ ΛΟΥΚΑ ΑΡΙΘΜΟΙ; ΑΡΙΘΜΟΙ ΚΑΡΜΙΚΑΕΛ; ΣΥΜΒΟΛΟ ΛΕΖΑΝΤΡΕ; ΣΥΜΒΟΛΟ ΓΙΑΚΟΒΙ; Λ-ΣΕΙΡΕΣ; ΨΕΥΔΟΠΡΩΤΟΙ; ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ; Prime Numbers; Diophantine Equations; Congruences; Quadratic Residues; Law Of Quadratic Reciprocity; Primitive Roots; Indexes; Primality Testing; Factorization; Continued Fractions; Pell Equation; Quadratic Forms; Quadratic Number Fields; Coding Theory; Integral Basis; Discriminant; Fundamental Unit; Decomposition Law; Class Number; Pseudoprimes; Carmichael Numbers; Jacobi Symbol; L-series; Legendre Symbol; Fibonacci And Lucas Numbers; Cryptography

This book is an introduction to number theory. Emphasis has been given to the historical development of the ideas and to applications. The book covers the teaching needs of all Mathematics departments in Greece. Until the ninth chapter only elementary tools are needed. <br/>Last chapter requires some knowledge of algebra and Galois theory. <br/><br/>Number theory for centuries was considered as part of "pure mathematics". The last 35 years many applications of number theory to cryptography and coding theory were discovered, and some of these applications are explained. <br/><br/>The book is divided into two parts. The first part is devoted to the arithmetic of natural numbers and the second part to the arithmetic of irrational quantities.