The problem "Unequally Yoked" looks for all integral solutions for a^b = b^a. But of course, there are a lot of non-integral solutions. If I graph the solution set where a and b are both greater than 0, I get two intersecting curves. Where do the two curves cross?

The first curve, as stated previously, is the line a=b.

The other curve looks roughly like a hyperbola, runs through the points (2,4) and (4,2), and (e,e).  

To see this, I used the Goal Seek function of Excel.  I started with a value for 'a' (such as 3.9) and then set the function a^b - b^a to zero, by varying 'b'.

Posted by Larry on 2005-04-25 22:20:15