modular arithmetic

The Math of Time In the Chapter on Set Theory, we discussed the idea of relations1 and specifically provided the example of modular equivalence on this page. In there we stated that the relation $$ a\equiv b \mod n $$ was true if both $a,b$ had the same remainder when divided by $n$.

Continuing Where We Left Off On this page we will discuss some theorems and topics that are slightly more advanced and would likely scare 👻 anyone away. Remember that equivalence $\mod n$ is literally an equivalence relation, that means we can actually create equivalence classes of items that are all equivalent to each other.

Euler’s Totient Function In this page we will discuss some interesting properties, and get us to the point that we need in order to understand RSA Encryption from scratch. Now that we have a distinction between residue classes and prime residue classes, we can see that some numbers seem to be “less prime” than other numbers.

What is RSA Encryption 📬 We’ve gone through a solid amount of number theory so far, and its crazy to think that this actually has a direct application in computer science, but it does.