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accepted Updated: finding an integer $k$ that minimizes $1/(N-k) (1+1/k)$
May
24
comment Updated: finding an integer $k$ that minimizes $1/(N-k) (1+1/k)$
Hi Safoura, thanks for your answer. But there is some problem here. Note that I have $k^* = \lceil \sqrt{aN+a^2 + 1/4} - a - 1/2 \rceil$, where $\lceil x \rceil$ is the ceiling function, denotes the smallest integer no less than $x$. While $k^* = [\sqrt{aN+a^2} - a]$, where $[x]$ is the rounding function, the integer closest to $x$. So your proof seems do not apply ...
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asked Updated: finding an integer $k$ that minimizes $1/(N-k) (1+1/k)$