Abstract (EN)
This thesis consists of fundamentally two chapters and these chapters consist of subchapters in itself. In the first chapter, triangular numbers and how they emerge are introduced as well as some important properties of them are mentioned. Also, some equations obtained from properties of triangular numbers are characterized.In the second chapter, square-triangular numbers are introduced and their close relations between Pell, Pell-Lucas numbers and {un}, {vn}, {yn} sequences are mentioned. Formula used to get square-triangular numbers is proved easily by means of some Diophantine equations. Monotone increasing, congruences and divisibility properties of Pell, Pell-Lucas, {un} and {vn} sequences and some new theorems are given. Solutions of some Diophantine equations are characterized and it is proved that these solutions are related to {un} and {vn} sequences. Moreover, it is showed that there exists no solution of the equality of ynym=yr for n>1 and m>1.
Author
Dr. Olcay Karaatlı
How to Cite
Olcay Karaatlı (Master Thesis). Triangular numbers, 2010, Sakarya University.
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