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Switzerland Team Selection Test
1999 Switzerland Team Selection Test
8
sum a_k = 96, sum a_k^2 = 144, sum a_k^3 = 216
sum a_k = 96, sum a_k^2 = 144, sum a_k^3 = 216
Source: Switzerland - Swiss TST 1999 p8
February 19, 2020
Sum
system of equations
algebra
Problem Statement
Find all
n
n
n
for which there are real numbers
0
<
a
1
≤
a
2
≤
.
.
.
≤
a
n
0 < a_1 \le a_2 \le ... \le a_n
0
<
a
1
≤
a
2
≤
...
≤
a
n
with
{
∑
k
=
1
n
a
k
=
96
∑
k
=
1
n
a
k
2
=
144
∑
k
=
1
n
a
k
3
=
216
\begin{cases} \sum_{k=1}^{n}a_k = 96 \\ \\ \sum_{k=1}^{n}a_k^2 = 144 \\ \\ \sum_{k=1}^{n}a_k^3 = 216 \end{cases}
⎩
⎨
⎧
∑
k
=
1
n
a
k
=
96
∑
k
=
1
n
a
k
2
=
144
∑
k
=
1
n
a
k
3
=
216
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