Determine all possible pair(s)

** (X, Y)** of positive integers that satisfy this equation.

**X**^{XX} = Y^{Y}
*Note*: The order of calculation in

**X**^{XX} is as given in

**this article**.

I found the link confusing. It seems to say that a "tower" of abc is to be read as a^^(b*c), assuming the dot operator is multiplication. I would have thought the likely confusion would be between (a^^b)^^c and a^^(b^^c). Phrases like "right to left" and "top down" are not self-explanatory on this. I would assume that right to left, or top down would be the latter of these expressions, but the illustrated examples are not clear (to me).

In any case, I think that IF there is a solution other than (1,1), it would most likely be if x and y each were of 10^^n format. Then the three-term and the two-term expressions would each be a single "1" followed by a number of "0"s. (I am accustomed to the COBOL exponent operator "**" rather than "^^".) Would the problem be more amenable to search if all operations were performed on binary operands?

*Edited on ***March 18, 2009, 7:42 pm**