Question 69
Given a positive integer $k$, let $\|k\|$ denote the absolute difference between $k$ and the nearest perfect square. For example, $\|13\|=3$ since the nearest perfect square to $13$ is $16$. Compute the smallest positive integer $n$ such that
$$
\frac{\|1\|+\|2\|+\cdots+\|n\|}{n}=100.
$$
Proposed by: Carl Schildkraut
$$
\frac{\|1\|+\|2\|+\cdots+\|n\|}{n}=100.
$$
Proposed by: Carl Schildkraut