SE-SKOLORNAS 1965 Problem 3

Show that for every real $x \ge \frac12$ there is an integer $n$ such that $|x - n^2| \le \sqrt{x-\frac{1}{4}}$ .

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.