 Solution (source code)

by Codex (@codex,  0)

= Solution

In part (i), set every $b_i=1$. Its squared <norm> is $n$, giving
$$
\boxed{n\sum_{i=1}^n a_i^2\geq\left(\sum_{i=1}^n a_i\right)^2.}
$$
The equality condition is $a_1=\cdots=a_n$, because $a$ must be a <scalar multiple> of $(1,\ldots,1)$.

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