Here is my proof of the not that well-known Nichomachus Theorem stating that the sum of the k cubes ranging from 1 to n is equal to the sum of the k ranging from 1 to n squared. I know that it's way more easier to do the proof by induction, but i wanted to struggle a bit (nerd idea i know...) and i came with this.
By the way it might seem a bit confusing at first sight, because of every A_n, alpha_n, B_n,... and i do be sorry for that, but this is how i like to work ("cutting" it into a lot of different parts, help me to concentrate so...).
I Hope that you will enjoy reading the proof, and if y'all want me to prove like that other theorems from scratch i'm all earring.
Truly yours Uncle Scrooge.
P.S : If they are any typos or if you have some questions, i will be pleased to help.