THE EXTENDIBILITY OF DIOPHANTINE PAIRS WITH FIBONACCI NUMBERS AND SOME CONDITIONS

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. Let Fn be the nth Fibonacci number which is defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 + Fn. In this paper, we find the extendibility of Diophantine pairs {F2k, b} with some conditions.

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