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Identifier

000397586

Title

Αναδρομικές ακολουθίες και θεωρία αριθμών

Alternative Title

Recursion sequences and number theory

Author

Καπνόπουλος, Εμμανουήλ

Thesis advisor

Αντωνιάδης, Ιωάννης

Reviewer

Τζανάκης, Νικόλαος
Κουρουνιώτης, Χρήστος

Abstract

In this master thesis we study about recursion sequences and especially those whose order is two. In the first chapter we construct a general theory about recursion sequences, we define the order of the sequence and its characteristic equation. We see how the general term of the sequence is expressed by using the roots of the equation. In the second part, we define the “Lucas sequences”. These are the generalization of the Fibonacci and Lucas sequences. We prove their identities and using them, we prove the “Lucas-Lehmer” test for Mersenne primes. In the final part, we see which terms are triangular numbers in the sequences of Fibonacci, Lucas and Pell. Through this, we give all the integer solutions of some Diophantine equations.

Language

Greek

Subject

Diophantine equation

Fibonacci

Generalized Lucas sequence

Sum of the first terms

Γενικευμένες ακολουθίες Lucas

Διοφαντική εξίσωση

Issue date

2015-11-20

Collection