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23
SMT 2010 General #23
SMT 2010 General #23
Source:
February 11, 2012
Problem Statement
Let
f
(
X
,
Y
,
Z
)
=
X
5
Y
−
X
Y
5
+
Y
5
Z
−
Y
Z
5
+
Z
5
X
−
Z
X
5
f(X, Y, Z)=X^5Y-XY^5+Y^5Z-YZ^5+Z^5X-ZX^5
f
(
X
,
Y
,
Z
)
=
X
5
Y
−
X
Y
5
+
Y
5
Z
−
Y
Z
5
+
Z
5
X
−
Z
X
5
. Find
f
(
2009
,
2010
,
2011
)
+
f
(
2010
,
2011
,
2009
)
−
f
(
2011
,
2010
,
2009
)
f
(
2009
,
2010
,
2011
)
\frac{f(2009, 2010, 2011)+f(2010, 2011, 2009)-f(2011, 2010, 2009)}{f(2009, 2010, 2011)}
f
(
2009
,
2010
,
2011
)
f
(
2009
,
2010
,
2011
)
+
f
(
2010
,
2011
,
2009
)
−
f
(
2011
,
2010
,
2009
)
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