be real numbers such that 
.
of positive integers such that 
and 
are both powers of 
.
and 
such that 
are the lengths of a right triangle.
![\[
\frac{(x+y+z)^5 - x^5 - y^5 - z^5}{(x+y)(y+z)(z+x)} = 0
\]](http://latex.artofproblemsolving.com/7/8/f/78f8e6c2570684631dc288144e13568d71e68ec8.png)
and 
play a series of of 
games. Each game either results in a win or loss for 
with 
such that
.
from the domain 
and put those numbers into the given function f(x)=1/x.It gives us 1=1/2.But it's not true.So ,it can't be one-one function.But in the answer,it is one-one function.Would anyone enlighten me where is my fault? Thank you!
.
and 
.
be reals such that 
. Prove that
Let 
. Prove that
Y by
A convex polyhedron 
is given in coordinate space. Is it true, that one can necessarily choose such a (possibly degenerate) a parallelepiped 
lying in such that the number of integer points inside and inside differ by no more than a million times?
I.Bogdanov, MathOverflow
is given in coordinate space. Is it true, that one can necessarily choose such a (possibly degenerate) a parallelepiped 
lying in such that the number of integer points inside and inside differ by no more than a million times?I.Bogdanov, MathOverflow
