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 Solution & Spoiler by e.g.)

The problem asks where the two curves cross, which many would interpret as calling for a point of intersection. This would be the point where q "=" 1 which is what? The limit of q^(1/(q-1)) as q goes to 1 appears to be needed. If we let q=1+1/v, then q^(1/(q-1))=(1+1/v)^v which goes to e=2.718... as v goes to infinity.  It looks like the intersection point sought is (e,e) then.

Posted by Richard on 2005-04-24 18:39:43