SE-SKOLORNAS 1998 Problem 5

Show that for any $n > 5$ we can find positive integers $x_1, x_2, ... , x_n$ such that $\frac{1}{x_1} + \frac{1}{x_2} +... + \frac{1}{x_n} = \frac{1997}{1998}$ . Show that in any such equation there must be two of the $n$ numbers with a common divisor ( $> 1$ ).