The Mathematics Blog by Nilo de Roock

$$p / ( p-1 ) ! + \left(\frac{a}{p}\right)  a^{(p-1)/2}$$ Proof. Consider the equation $Ax \equiv a \bmod p$ with $A, x \in \{ 1,2, \cdots...

I had one again. I am still in awe. I used to call them "cognitions", but that's not enough. The right word is epiphany. The p...

Let $ p \in \mathbb {Z}[X] $ and of fifth degree with only the terms for $x^5$, $x^4$ and $x^3$ known, the terms for $x^2$, $x$ and $1$ are ...

It's time to read Gauss's original work. More later.

A few years ago I wanted to find a 5 by five magic square. I gave up on it. See this post for the results I came up with in 2011. I used t...

ARE YOU INFECTED WITH MV/C ? What is MV A mathematical virus (MV) is a preconception about the structure, function or method of mathematics ...

Uni-color-2D graphics can't be spectaculair, let alone breathtaking. Unless you are in the know. Let me explain. I am now able to - almo...

I learned that 0,999... = 1. I believe it was in M381 that I learned to prove it. The proof is quite simple actually. Let x = 0,999..., m...

If you read the previous posts on my tiling printing algorithms you'll understand the reason for this post: I made some progress that un...

If only Mindjet's MindManager could handle LaTeX it would be the perfect tool for organizing my notes, unfortunately it can't and th...

As an OU student you have to make several TMAs for each course you do. TMA stands for Tutor Marked Assignment. A TMA consists of assignments...

I developed an algorithm that takes sequences like $\{ 6, 2, 4, 3, 3, 2, 4, 2, 3, 2, 3, 3, 4, 4, 3, 3, 4 \}$ and turns them into drawings...