There are no Diophantine quadruples of Fibonacci numbers

Abstract

We show that there is no Diophantine quadruple, that is, a set of four positive integers {a 1 , a 2 , a 3 , a 4 } such that a i a j + 1 is a square for all 1 ≤ i < j ≤ 4, consisting of Fibonacci numbers.