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.

Here's a formula for finding the equivalence class of any positive integer for any Mod, for example: What is 337 Mod 11? We know 337 / 11 has a quotient of 30 with a remainder. 337 - 11 * 30 = 7, so 337 = …

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.

Can anyone help me? I understand modulo arithmetic but I cannot understand congruence modulo and how to solve this. It is really frustrating.

This has given us a method to calculate A^B mod C quickly provided that B is a power of 2. However, we also need a method for fast modular exponentiation when B is not a power of 2.

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.

In this lesson, we'll be learning two new ways to represent arithmetic sequences: recursive formulas and explicit formulas. Formulas give us instructions on how to find any term of a sequence.

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

In this lesson, we'll be learning two new ways to represent arithmetic sequences: recursive formulas and explicit formulas. Formulas give us instructions on how to find any term of a sequence.

If the the modulus is large, trying to find the modular inverse by brute force could take an extremely long time i.e. longer than your lifetime So for small numbers, brute force may be easier, but for big …