# Solution: 2019-19 Balancing consecutive squares

Find all integers $$n$$ such that the following holds:

There exists a set of $$2n$$ consecutive squares $$S = \{ (m+1)^2, (m+2)^2, \dots, (m+2n)^2 \}$$ ($$m$$ is a nonnegative integer) such that $$S = A \cup B$$ for some $$A$$ and $$B$$ with $$|A| = |B| = n$$ and the sum of elements in $$A$$ is equal to the sum of elements in $$B$$.

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