Abstract
Let Fn denote the n-th Fibonacci number, and pi the i-th prime number. In this paper, we consider the Diophantine equation Fn1 + Fn2 + Fn3 = pz11 · · · pzss in non-negative integers n1 ≥ n2 ≥ n3 ≥ 0 and non-negative integers zi with 1 ≤ i ≤ s. In particular, we completely solve the case that s = 12.
| Original language | English |
|---|---|
| Pages (from-to) | 407-434 |
| Number of pages | 28 |
| Journal | Publicationes Mathematicae Debrecen |
| Volume | 103 |
| Issue number | 3-4 |
| Publication status | Published - 2023 |
Keywords
- diophantine equations
- fibonacci sequences
- linear forms in logarithms
- recurrence sequences