Question 877519
<pre>
{{{xy/(x+y)}}}{{{""=""}}}{{{24}}}

xy - 24y = 24x

 y(x-24) = 24x

       y = {{{24x/(x-24)}}}

Divide that out by long division:

    <u>      24</u>
x-24)24x+  0
     <u>24x-576</u>
         576

       y = 24 + {{{576/(x-24)}}}

We can set the denominator x-24 equal to any factor of 576
and solve for x, which will give us a positive integer value 
for y.

576 = 2<sup>6</sup>3<sup>2</sup>

So by the formula for the number of factors, 576 has (6+1)(2+1) = 21
factors.

Therefore there are 21 ordered pairs (x,y)

Answer = 21.

Edwin</pre>