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.

 5   point 16
10   for T=1 to 1100
20       for X=1 to int(T/2)
30         Y=T-X
40         Lhs=X^X*log(X):Rhs=Y*log(Y)
50         Diff=abs(Lhs-Rhs)
60         if Diff<0.00000000001 then print X;Y
70       next X
80   next T

checks all x and y where x+y totals 1100 or less and finds only (1,1)

The point 16 gives fractions to 77 decimal places.

Posted by Charlie on 2009-03-18 13:46:28