SE-SKOLORNAS 1982 Problem 1

How many solutions does $x^2 - [x^2] = \left(x - [x]\right)^2$ have satisfying $1 \leq x \leq n$ ?

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.