Development of the Properties of Divisibility and Exact Divisibility by Powers of the Integers in the Lucas Sequences of the First and Second Kinds
Keywords:
Divisibility, Exact divisibility, Fibonacci sequence, Lucas sequence, Recurrence relation, Lucas sequence of the first kind, Lucas sequence of the second kindAbstract
This article provides a comprehensive compilation and organization the properties of divisibility and exact divisibility by powers of the integers in the Fibonacci sequence, Lucas sequence, and other recurrence relations. It also explores properties related to the development of divisibility properties and exact divisibility by powers of the integers in the Lucas sequences of the first and second kinds. By exploring the development of these properties from 1970 to 2021, it highlights the contributions of numerous researchers over this 51-year period and identifies avenues for future research.
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