Abstract
A set {a1, a2, …, am} of positive integers is called a Diophantine m-tuple if aiaj + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we prove that if {F2k, F2k+4, c} is a Diophantine triple then there is a unique positive integer d such that c < d and {F2k, F2k+4, c, d} is a Diophantine quadruple.
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