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Jozsef Wildt International Math Competition
2009 Jozsef Wildt International Math Competition
W. 18
prove this cyclic inequality
prove this cyclic inequality
Source: 2009 Jozsef Wildt International Mathematical Competition
April 26, 2020
inequalities
Problem Statement
If
a
a
a
,
b
b
b
,
c
>
0
c>0
c
>
0
and
a
b
c
=
1
abc=1
ab
c
=
1
, then
∑
c
y
c
a
+
b
+
c
n
a
2
n
+
3
+
b
2
n
+
3
+
a
b
≤
a
n
+
1
+
b
n
+
1
+
c
n
+
1
\sum \limits^{cyc} \frac{a+b+c^n}{a^{2n+3}+b^{2n+3}+ab} \leq a^{n+1}+b^{n+1}+c^{n+1}
∑
cyc
a
2
n
+
3
+
b
2
n
+
3
+
ab
a
+
b
+
c
n
≤
a
n
+
1
+
b
n
+
1
+
c
n
+
1
for all
n
∈
N
n\in \mathbb{N}
n
∈
N
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