Abstract
We consider sequences of integers formed by a quotient of the Lucas sequences or elliptic divisibility sequences. We then investigate some divisibility properties of these quotient sequences. Additionally, we prove that elliptic divisibility sequences possess a divisibility property that is analogous to a generalization of Matijasevich’s lemma involving the Fibonacci numbers, which contributed to the solution to Hilbert’s tenth problem.
| Original language | English |
|---|---|
| Article number | 22.9.2 |
| Journal | Journal of Integer Sequences |
| Volume | 25 |
| Issue number | 9 |
| Publication status | Published - 2022 |
Keywords
- Fibonacci number
- Hilbert’s tenth problem
- Lucas number
- Matijasevich
- almost strong divisibility sequence
- elliptic divisibility sequence
- strong divisibility sequence
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