For what values of <i>a</i> and <i>b</i> (where <i>a</i> and <i>b</i>
are positive integers) do the two equations:



<br clear="all" /><table border="0" width="100%"><tr><td>
<table border="0" width="80%" align="right"><tr><td nowrap="nowrap" align="right">
<table border="0"><tr><td nowrap="nowrap" align="left">
\x<sup>2</sup><font face="symbol">-</font
><i>ax</i>+<i>b</i></td></tr></table></td><td nowrap="nowrap" align="left">
<table border="0"><tr><td nowrap="nowrap" align="left">
=0 </td></tr></table></td></tr><tr><td nowrap="nowrap" align="right" colspan="1"><table border="0"><tr><td nowrap="nowrap" align="left">
 <i>x</i><sup>2</sup><font face="symbol">-</font
><i>bx</i>+<i>a</i></td></tr></table></td><td nowrap="nowrap" align="left">
<table><tr><td nowrap="nowrap" align="right" colspan="1">=0 </td></tr></table></td></tr></table>
</td></tr></table>

 both have
positive integer solutions? You may be able to
find some values of <i>a</i> and <i>b</i> by trial and
error. Can you prove that these are the only
possible values?