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.

If you gobble a gaggle of gerbils, and gurgle while gargling a giggle of goggles (oh, that was yesterday...), the denouement devolves.  Think of googols and googleplexes.  Since the two sides of the equation must be composed of the same factors, it seems x and y must be powers of 10 (e.g. power zero gives 1,1 -- the only obvious solution).

Why did KS give us a link to 20 pages of bafflement (and probably the less common interpretation of multiple exponentiations) when he could have saved us the trouble of searching that whole link for two lines which were to guide us here??

Alephs for Alfie!

Posted by ed bottemiller on 2009-03-18 15:42:16