# Entries

## Barcode restoration and division modulo a prime

Yesterday, I came across a puzzle in which we had to decode a barcode (Code 128) of which a piece had been obfuscated. The math involved in this is very elegant, so I decided to write it down, hoping that one day someone will benefit from it.

## Repeated substitution and Chebyshev polynomials

Recently, I was experimenting with a process in which we start with the polynomial $f_0(x) = x$ and obtain $f_n(x) = f_{n-1} \left(\frac{1}{s-x}\right)$ by substituting $x \mapsto \frac{1}{s-x}$, for some number $s \in \mathbb C$. By accident, I saw that both for $s=1$ and $s=-1$, $f_3 = f_0$. Of course, for $s=0$, $f_2 = f_0$ as well. This made me wonder: for which values of $s$ do we have $f_n = f_0$ for some $n>0$?

## Group theory 101.0

This is an introduction to group theory, covering the concepts of groups, subgroups and (homo)morphisms.

## Hello, World!

I am setting up this blog to share interesting stuff I find on the internet, in my books or in my lectures.