Question 116
For all positive integers $n$ and $m$ prove the inequality
$$
|n\sqrt{n^2+1} - m| \ge \sqrt{2} - 1.
$$
$$
|n\sqrt{n^2+1} - m| \ge \sqrt{2} - 1.
$$
MathNet 2018-part-01 — 181 problems (EN–VI) Question 116
Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)