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?

(In reply to re: Solution & Spoiler by Richard)

Technically, the intersection would be a 2-D curve, not a 1-D point. Think of it this way. Let:

z1=x^y
z2=y^x

Each one is a 3-D curve. The intersection of these 3-D curves is a 2-D curve. e.g. expresses this curve as parametric equations. It just so happens this expression cannot include x=y. So we can easily just say there are 2 curves.

Posted by np_rt on 2005-04-25 03:33:39