OSN 2003 Problem 3

Find all real numbers $x$ such that $\left\lfloor x^2 \right\rfloor + \left\lceil x^2 \right\rceil = 2003$ .

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.