BY-MO 2018 Problem 96

For all positive integers $m$ and $n$ prove the inequality $|n\sqrt{n^2+1}-m|\geqslant \sqrt{2}-1.$

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.