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Exponent Crossed Power (Posted on 2009-03-18) Difficulty: 3 of 5
Determine all possible pair(s) (X, Y) of positive integers that satisfy this equation.

                                        XXX = YY

Note: The order of calculation in XXX is as given in this article.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Some Thoughts computer exploration | Comment 2 of 10 |

 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
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