Παραγοντοποίηση Ακεραίων

• Main Authors: Πουλάκης, Δημήτριος, Poulakis, Dimitrios
• Format: 7
• Language: Greek
• Published: 2016
• Subjects: ΥΠΟΛΟΓΙΣΤΙΚΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ; ΣΥΝΕΧΗ ΚΛΑΣΜΑΤΑ; Computational Number Theory; Continuous Fractions

Chapter 2 is devoted to the theory of continuous fractions. More precisely, we study the presentation of the rational in finite continuous fraction and the presentation of irrationals in infinite continuous fractions. We prove that the sequence of convergent fractions of the infinite<br/>fraction of an irrational number converges to this number and we give a sufficient condition for a rational number to be a convergent fraction of the continuous fraction of a number. Furthermore, we prove that a quadratic irrational if and only if the sequence of the terms of its continuous fraction is periodic.