There are no Diophantine quadruples of Fibonacci numbers
Volume 185 / 2018
Acta Arithmetica 185 (2018), 19-38
MSC: Primary 11D09; Secondary 11B39.
DOI: 10.4064/aa170613-8-12
Published online: 18 June 2018
Abstract
We show that there is no Diophantine quadruple, that is, a set $\{a_1,a_2,a_3,a_4\}$ of four positive integers such that $a_ia_j+1$ is a square for all $1\le i \lt j\le 4$, consisting of Fibonacci numbers.
