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Greece Junior Math Olympiad
1998 Greece Junior Math Olympiad
2
Greece Junior National Olympiad 1997-98 problem 2
Greece Junior National Olympiad 1997-98 problem 2
Source:
August 10, 2015
inequalities
Problem Statement
If
a
1
,
a
2
,
.
.
.
.
,
a
n
−
1
,
a
n
a_1, a_2,...., a_{n-1}, a_n
a
1
,
a
2
,
....
,
a
n
−
1
,
a
n
, are positive integers, prove that:
∏
i
=
1
n
(
a
i
2
+
3
a
i
+
1
)
a
1
a
2
.
.
.
.
a
n
−
1
a
n
≥
2
2
n
\frac{\prod_{i=1}^n(a_i^2+3a_i+1)}{a_1a_2....a_{n-1}a_n}\ge 2^{2n}
a
1
a
2
....
a
n
−
1
a
n
∏
i
=
1
n
(
a
i
2
+
3
a
i
+
1
)
≥
2
2
n
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