Abstract
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.
| Original language | English |
|---|---|
| Article number | 10 |
| Number of pages | 10 |
| Journal | Rose-Hulman Undergraduate Mathematics Journal |
| Volume | 21 |
| Issue number | 1 |
| Publication status | Published - 2020 |
| Externally published | Yes |
Keywords
- Cycles
- Fibonacci sequences
- Modular arithmetic
- Recurrence relations