Abstract
A set of positive integers {; ; a1, a2, ..., a_m}; ; with the property that a_i*a_j+1 is a perfect square for all distinct indices i and j between 1 and m is called Diophantine m-tuple. In this paper, we show that if {; ; a, b, c, d, e}; ; is a Diophantine quintuple with a 3ag ; moreover, if c > a + b + 2\sqrt{; ; ab + 1}; ; then b > max{; ; 24 ag, 2a^1.5g^2}; ; . Similar results are given assuming that either ab is odd or c = a + b + 2\sqrt{; ; ab + 1}; ; .
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