# The Chessboard From Greece!

For an even positive integer $$n<10000$$, we write down all the numbers $$1, 2, 3, \ \ldots\ , n^2$$ on the squares of an $$n\times n$$ chessboard.

Let $$S_1$$ be the sum of all the numbers written on black squares and $$S_2$$ be the sum of all the numbers written on white squares.

How many possible values of $$n$$ are there such that it is possible to achieve

$\frac{S_1}{S_2}=\frac{39}{64}?$

Details and assumptions:

Each number appears exactly once on the board.

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