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JBMO ShortLists
2012 JBMO ShortLists
5
5
Part of
2012 JBMO ShortLists
Problems
(1)
Largest n
Source: JBMO Shortlist 2012 A5
2/4/2015
Find the largest positive integer
n
n
n
for which the inequality
a
+
b
+
c
a
b
c
+
1
+
a
b
c
n
≤
5
2
\frac{a+b+c}{abc+1}+\sqrt[n]{abc} \leq \frac{5}{2}
ab
c
+
1
a
+
b
+
c
+
n
ab
c
≤
2
5
holds true for all
a
,
b
,
c
∈
[
0
,
1
]
a, b, c \in [0,1]
a
,
b
,
c
∈
[
0
,
1
]
. Here we make the convention
a
b
c
1
=
a
b
c
\sqrt[1]{abc}=abc
1
ab
c
=
ab
c
.
inequalities
inequalities proposed