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 $k=2,3$.
how many natural numbers on a sphere
3
$\begingroup$
diophantine-equations
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0Have 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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0Also related: http://math.stackexchange.com/questions/88826/integer-coordinate-set-of-points-that-is-a-member-of-sphere-surface?lq=1 – 2012-09-21
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0See http://mathworld.wolfram.com/SumofSquaresFunction.html – 2012-09-21