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.
(In reply to
computer exploration by Charlie)
Since the LHS increases so much more rapidly than the RHS, it doesn't make sense to treat x and y equivalently. So:
10 point 16
20 X=1:Y=1
30 loop
40 Lhs=(X^X)*log(X):Rhs=Y*log(Y)
50 Diff=abs(LhsRhs)
60 if Diff<0.000000001 then print X;Y
70 if Lhs=Rhs then inc X:inc Y:else if Lhs<Rhs then inc X:else inc Y
80 endloop
had still found only (1,1) by the time it was stopped with x=10 and y=57,090,100

Posted by Charlie
on 20090318 15:19:52 