THE EXTENDIBILITY OF DIOPHANTINE PAIRS WITH FIBONACCI NUMBERS AND SOME CONDITIONS

A set {a_1, a_2, cdots, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j+1 is a perfect square for all 1leq i < j leq m. Let F_n be the nth Fibonacci number which is defined by F_0=0, F_1=1 and F_{n+2}=F_{n+1}+F_n. In this paper, we find the extendibility of Diophantine pairs {F_{2k}, b} with some conditions.