On Diophantine quadruples of Fibonacci numbers

Abstract

Abstract. We show that there are only finitely many Diophantine quadruples, that is, sets 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.