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

Posted by ed bottemiller on 2009-03-18 19:38:19