I came across this fun theorem in a talk about tree colorings: Combinatorial Nullstellensatz. Let $f \in F[x_1, x_2, \ldots, x_n]$ be a polynomial of degree $t_1 + \cdots + t_n$. If $S_1, S_2, \ldots, S_n$ are nonempty subsets of $F$ such that $\left| S_i \right| \geq t_i . . . Read more

I came across this video by NumberPhile and 3Blue1Brown about the density of primes that are 1 mod 4 vs the density of primes that are 3 mod 4. The main fact is quite cool but there was something that he said during in the middle of t . . . Read more

I came across this “one sentence” proof that every prime congruent to 1 mod 4 can be written as a sum of two squares: https://doi.org/10.2307/2323918 The proof involves constructing the following cryptic involution $$ (x, y, . . . Read more