On the Periods of Biperiodic Fibonacci and Biperiodic Lucas Numbers

Abstract

This paper is concerned with periods of Biperiodic Fibonacci and Biperiodic Lucas sequences taken as modulo prime and prime power. By using Fermat’s little theorem, quadratic reciprocity, many results are obtained.

Bi-Periodic Balancing Quaternions

“…There are so many researches on integer sequences such as Fibonacci, Lucas and Jacobsthal sequences [7][8][9]11]. By the view of the definition of quaternions, the quaternions of some integer sequences was defined.…”