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An equation (
Posted on 20140703
)
The equation x
^{x}
y
^{y}
=z
^{z}
has trivial integer solutions if x=1 or y=1. What is the smallest solution to x
^{x}
y
^{y}
=z
^{z}
where x, y, and z are integers and 1<x≤y?
No Solution Yet
Submitted by
Math Man
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Comments: (
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)
re(2): solution
Comment 5 of 5 
(In reply to
re: solution
by broll)
Yes, I mistakenly used '+' when I should have used '*'.
Instead, (az)^a * (bz)^b = z
and a^a * b^b * z^(a+b1) = 1
requiring a=b=1 and z=1.
Posted by
xdog
on 20140714 10:33:23
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