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For a given $n \in \mathbb{N}$, consider the algebraic function: $$ f_n : \mathbb{R}^{n+2} \rightarrow \mathbb{C} $$ $$ f_n(x,y,z_1,\dots,z_n) = x + iy $$ We're going to define a 'simple period' to be …

Recall the quartic version of the Cayley-Bacharach theorem: Theorem: Consider two quartics in general position, which intersect in $16$ points (by Bezout's theorem). Then if a third quartic passes th …

Does there exist an irreducible polynomial $f \in \mathbb{R}[x, y, z]$ such that: $$ V := \{ (x, y, z) \in \mathbb{R}^3 : f(x, y, z) \leq 0 \} $$ is a solid of constant width with a finite symmetry gr …

A graph $G$ is described as a unit-distance graph if there exists a function $f:G \rightarrow \mathbb{C}$ such that for every edge $(u,v) \in E(G)$, we have $|f(u) - f(v)| = 1$. Obviously, we can nec …

The integrand is periodic modulo $\pi$ in each variable, so it suffices to integrate each variable over $[0, \pi]$ and replace the constant factor by $2^{-7}$. If we were to apply a change of variabl …

The following comment in the question intrigued me: In fact, it's possible to show that the linear symmetries of $\mathbb{R}^6$ that preserve the Cayley-Menger determinant form the Weyl group $D_6$, …

Yes. I'll talk about why elliptic curve discrete log is harder than ordinary discrete log. Suppose we have $g, h$ and want to find $n$ such that $g^n = h$. The usual methods for solving the discrete …