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International Contests
Austrian-Polish
1999 Austrian-Polish Competition
2
Find the best constants
Find the best constants
Source: Austrain Polish 1999
December 7, 2013
inequalities unsolved
inequalities
Problem Statement
Find the best possible
k
,
k
′
k,k'
k
,
k
′
such that
k
<
v
v
+
w
+
w
w
+
x
+
x
x
+
y
+
y
y
+
z
+
z
z
+
v
<
k
′
k<\frac{v}{v+w}+\frac{w}{w+x}+\frac{x}{x+y}+\frac{y}{y+z}+\frac{z}{z+v}<k'
k
<
v
+
w
v
+
w
+
x
w
+
x
+
y
x
+
y
+
z
y
+
z
+
v
z
<
k
′
for all positive reals
v
,
w
,
x
,
y
,
z
v,w,x,y,z
v
,
w
,
x
,
y
,
z
.
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