A modular circle of size -3 wouldn't make much sense. However, if we wanted to find out the remainder of A/B when B is negative, we can simply multiply A/B by -1/-1 to make B positive.

We will discuss the meaning of congruence modulo by performing a thought experiment with the regular modulo operator. Let's imagine we were calculating mod 5 for all of the integers: …

Let's explore the addition property of modular arithmetic: (A + B) mod C = (A mod C + B mod C) mod C Example: Let A=14, B=17, C=5

Most modern cryptography relies on modular arithmetic. Two notable example are RSA and Diffie Hellman. Older ciphers like the Caesar cipher, Vigenere cipher, and Affine ciphers use it too.

What is a modular inverse? In modular arithmetic we do not have a division operation. However, we do have modular inverses.

This says that A is congruent to B modulo C . It is similar to the expressions we used here, but not quite the same. In the next article we will explain what it means and how it is related to the …

Use fast modular exponentiation as described in the next lesson. Right after that lesson there is a calculator for modular exponents, so you can check your calculations.

Modular addition and subtraction Modular addition Modulo Challenge (Addition and Subtraction) Modular multiplication Modular multiplication Modular exponentiation Fast modular …

Computer science theory ... Modulo Challenge (Addition and Subtraction) Modular multiplication Modular multiplication Modular exponentiation

Modular addition and subtraction Modular addition Modulo Challenge (Addition and Subtraction) Modular multiplication Modular multiplication Modular exponentiation Fast modular …