A Pair of Diophantine Equations and Fibonacci-Like Sequences
Abstract
Given two relatively prime numbers a and b, it is known that exactly one of the two Diophantine equations has a nonnegative integral solution (x,y):ax+by = (a−1)(b−1)2 and 1+ax+by = (a−1)(b−1)2.Furthermore, the solution is unique. This paper surveys recent results on finding the solution and determining which equation is used when a and b are taken from certain sequences. We contribute to the literature by finding (x,y) when a and b are consecutive terms of sequences having the Fibonacci recurrence and arbitrary initial terms.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Advanced Mathematical Theories
Analytic Number Theory Research
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Pages
- 1–17
- Publication date
- 21 July 2026
- Language
- EN