Properties of the Fibonacci-Lucas Sequence Mod m
Submission Type
Event
Faculty Advisor
Andrew Shallue
Expected Graduation Date
2021
Location
Center for Natural Sciences
Start Date
4-4-2020 9:00 AM
End Date
4-4-2020 10:00 AM
Disciplines
Education | Mathematics
Abstract
The Lucas sequence is a variation of the Fibonacci sequence and connects to many similar properties. Using new methods of computation, a larger portion of the Lucas sequence is reduced by mod m and various patterns are compared to the known properties of the Fibonacci sequence. Analysis of the cyclic behavior and length of the Lucas sequence are studied using matrix notation. Specific properties pertaining to prime numbers are also noted for applications in cryptography.
Properties of the Fibonacci-Lucas Sequence Mod m
Center for Natural Sciences
The Lucas sequence is a variation of the Fibonacci sequence and connects to many similar properties. Using new methods of computation, a larger portion of the Lucas sequence is reduced by mod m and various patterns are compared to the known properties of the Fibonacci sequence. Analysis of the cyclic behavior and length of the Lucas sequence are studied using matrix notation. Specific properties pertaining to prime numbers are also noted for applications in cryptography.