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For questions that specifically ask for determining a closed form of equations, integrals etc.

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counting points on unit sphere mod p

Let $f(n)$ be the number of points on the unit sphere $x^2 + y^2 + z^2 = 1\; \pmod n$ with $x,y,z \in \mathbb{Z}/n\mathbb{Z}$ This is sequence A087784 in the Online Encyclopedia of Integer sequence …
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