MHB Finding Squares in a Square Box: n > 1

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Determine all integers n> 1, for which in the square box of dimensions (n x n) you can enter different squares of integers, so that the sum of numbers in each row and in each column of the array is a square of an integer, and all the 2n sums are different.
 
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I get a headache reading that...
can you PLEASE post an example...merci beaucoup...
 
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I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
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