Special Numbers, Special Quaternions and Special Symbol Elements

Abstract

In this paper we define and we study properties of (l, 1, p + 2q, q · l) − numbers, (l, 1, p + 2q, q · l) − quaternions, (l, 1, p + 2q, q · l) − symbol elements. Finally, we obtain an algebraic structure with these elements.

Properties and applications of some special integer number sequences

“…Let be a nonzero positive integer. Savin 19 considered the sequence , We call these numbers numbers or numbers. We remark that for it is obtained the Fibonacci numbers and, for , it is obtained the Pell numbers.…”

“…Remark Let be the sequence previously defined 19 . Then, the following relations are true: i) ii) For and , we obtain that called the Binet's formula for the sequence . …”