NL-NWO 1976 Problem 5

$f(k) = k + \left[ \frac{n}{k}\right ]$ , $k \in \{1,2,..., n\}$ , $k_0 =\left[ \sqrt{n} \right] + 1$ .

Prove that $f(k_0) < f(k)$ if $k \in \{1,2,..., n\}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.