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2100
Skibidi Numbers
Editorial
algebra
optimization
inequalities
Cauchy-Schwarz
sequences
A positive integer
N
N
N
is called skibidi if there exist positive reals
a
1
,
a
2
,
…
,
a
N
a_1, a_2, \ldots, a_N
a
1
,
a
2
,
…
,
a
N
satisfying
∑
k
=
1
N
k
2
a
k
=
4
and
∑
k
=
1
N
a
k
2
k
≤
1
100
.
\sum_{k=1}^{N} k^2 a_k = 4 \qquad \text{and} \qquad \sum_{k=1}^{N} \frac{a_k^2}{k} \le \frac{1}{100}.
k
=
1
∑
N
k
2
a
k
=
4
and
k
=
1
∑
N
k
a
k
2
≤
100
1
.
Find the minimum skibidi number
N
N
N
.
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