All Questions

Let $a$ be an element of some ring or field, possibly finite. Is there closed form for $\sum_{i=1}^n{a^{i^2}}$? sage and wolframalpha couldn't solve it. If $a$ is primitive n-th root of unity this is ...

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 ...