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National and Regional Contests
Korea Contests
Korea National Olympiad
1996 Korea National Olympiad
7
7
Part of
1996 Korea National Olympiad
Problems
(1)
This is kinda weird problem...
Source: 1996 Korea National Olympiad #7
3/22/2018
Let
A
n
A_n
A
n
be the set of real numbers such that each element of
A
n
A_n
A
n
can be expressed as
1
+
a
1
2
+
a
2
(
2
)
2
+
⋯
+
a
n
(
n
)
n
1+\frac{a_1}{\sqrt{2}}+\frac{a_2}{(\sqrt{2})^2}+\cdots +\frac{a_n}{(\sqrt{n})^n}
1
+
2
a
1
+
(
2
)
2
a
2
+
⋯
+
(
n
)
n
a
n
for given
n
.
n.
n
.
Find both
∣
A
n
∣
|A_n|
∣
A
n
∣
and sum of the products of two distinct elements of
A
n
A_n
A
n
where each
a
i
a_i
a
i
is either
1
1
1
or
−
1.
-1.
−
1.
algebra