DE-BUNDESWETTBEWERB 2007 Problem 5

Round 2

For which numbers $n$ is there a positive integer $k$ with the following property: The sum of digits for $k$ is $n$ and the number $k^2$ has sum of digits $n^2.$

Dataset text AI-MO AoPS. Quoted with source.

Official text: Bundeswettbewerb Mathematik 2007 official paper, page 1.

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