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
Titration or Tetration ? by ed bottemiller)
The link does lead you to the Identities and properties section of the article, and without scrolling you find
Similarly, while addition and multiplication are associative (for example, (2+3)+4 = 9 = 2+(3+4) and (2·3)·4 = 24 = 2·(3·4), exponentiation is not associative either: 2^{3} to the 4th power is 8^{4} or 4096, but 2 to the 3^{4} power is 2^{81} or 2,417,851,639,229,258,349,412,352. Without parentheses to modify the order of calculation, the order is usually understood to be topdown, not bottomup:
<DL>
<DD><IMG class=tex alt="a^{b^c}=a^{(b^c)}ne (a^b)^c=a^{(bcdot c)}=a^{bcdot c}." src="http://upload.wikimedia.org/math/d/8/b/d8b9a0216869860dcada1176ed40f5d7.png"> </DD></DL>

Posted by Charlie
on 20090318 15:54:16 