yes I see your point, as for solutions a=b^r with r not an integer I am still working on that part and wanted to submit what I had thus far.  I should have clarified that.  As for solutions outside of a=b^r since b^r is increasing continuous function in r for any integer b then for any integers a,b you can find a real number r such that a=b^r thus any solution can be represented in this way.  Now if negative solutions were to be considered then this would no longer hold for certain solutions like if a were negative and b positive.  As for the rest of my solution for when r is not an integer I am almost complete and I shall post it once I am finished

Posted by Daniel on 2006-07-24 09:17:38