NL-NWO 1985 Problem 2

Among the numbers $11n + 10^{10}$ , where $1 \le n \le 10^{10}$ is an integer, how many are squares?

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.