In this paper, we find patterns and count the number of distinct generalised Fibonacci sequences under modular arithmetic. We will start with the repetition of the normal Fibonacci sequence modulo an integer, m, where m is greater than or equal to two and make connections to its dependency on the prime factorisation of m. We will then extend the complexity of the problem into generalised Fibonacci sequences with different starting values. Finally we will present some interesting observations that are still open problems.
Ha Tran, Concordia University of Edmonton and Amy Feaver, the King’s University, Edmonton
"Generalised Fibonacci Sequences under Modular Arithmetic,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 21
, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss1/10