A Remark on a Paper of Luca and Walsh.

In 2002, F. Luca and P. G. Walsh studied the Diophantine equations of the form ( ak - 1)( bk - 1) = x2, for all ( a, b) in the range 2 ≤≤ b < a ≤≤ 100 with sixty-nine exceptions. In this paper, we solve two of the exceptions. In fact, we consider the equations of the form ( ak - 1)( bk - 1) = x2, with ( a, b) = (13, 4), (28, 13). [ABSTRACT FROM AUTHOR]