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such that 
are the lengths of a right triangle.
and 
play a series of of 
games. Each game either results in a win or loss for . Total number of ways in which can win the series is:
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!
be reals such that 
. Prove that
Let be reals such that 
. Prove that
![\[
\frac{(x+y+z)^5 - x^5 - y^5 - z^5}{(x+y)(y+z)(z+x)} = 0
\]](http://latex.artofproblemsolving.com/7/8/f/78f8e6c2570684631dc288144e13568d71e68ec8.png)
.
and 
.
positive integer arrays 
,
,