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how many natural solutions are there to the following equation: $$ \sum_{i=0}^k x_i^2 = n$$ where $n,k \in\ \Bbb{N}$
i well like to get a answer for every n and k, but could do with just $k=2,3$.

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    Have a look at http://math.stackexchange.com/questions/86178/integer-lattice-points-on-a-sphere and the links there.2012-09-21
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    Also related: http://math.stackexchange.com/questions/88826/integer-coordinate-set-of-points-that-is-a-member-of-sphere-surface?lq=12012-09-21
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    See http://mathworld.wolfram.com/SumofSquaresFunction.html2012-09-21

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