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Q:
Find lowest value of p in $a_1^2 + a_2^2 + a_3^2 + \cdots + a_n^2 \ge n$
I am looking for an optimized way to determine the number of $a_i$s satisfying the inequality
$$a_1^2 + a_2^2 + a_3^2 + \cdots + a_n^2 \ge n$$
The actual number of real numbers $a_i$ is very small, so brute-force is out of the question.
A:
We have
\begin{align}
a_1^2 + \cdots + a_n^2
&\ge n
\iff \\[6pt]
a_1^2 + \cdots + a_n^2
&\le \sqrt{n}\sqrt{n}
= n
\iff \\[6pt]
a_1^2
6d1f23a050
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