Compute using integers:

Compute using an offset:

Mod works on integers:

Rational numbers:

Real numbers:

Complex numbers:

Exact numbers:

Inexact number:

Compute using large integers:

Mod threads over lists:

TraditionalForm formatting:

Solve a modular equation:

Use Mod in a sum:

Product:

Simplify an expression:

Identify Mod sequences:

Recurrence equation:

DirichletTransform:

Generating function:

The first 20 values of Mod:

Plot the sequence with a fixed modulus:

Plot the sequence, varying the modulus:

Generating function of Mod[n,8]:

Exponential generation function:

Dirichlet series:

Given an International Standard Book Number (ISBN), check whether or not it is valid:

An ISBN is valid if , where each is the digit of the ISBN:

Check if each of the ISBNs are valid:

Build an RSA-like encryption scheme. Start with the modulus:

Find the universal exponent of the multiplication group modulo n:

Private key:

Public key:

Encrypt a message:

Decrypt it:

Use Mod to create a Caesar cipher that shifts letters in the alphabet to encrypt a message:

Encrypt a message with a key:

Decrypt the message:

Check if numbers of the form are prime or composite:

Select primes below 100 having the form of :

Fermat's little theorem:

Euler's theorem:

Wilson's theorem:

Define a notation for addition modulo 2:

Use Mod to solve systems of linear congruences:

Create a random number generator that uses the current time as a seed:

Choose a modulus and base:

Compute 1000 random numbers between 0 and 1:

Extract parts of a list cyclically:

Modular computation of a matrix inverse:

First compute the matrix adjoint:

Then compute the modular inverse of a matrix:

Check that the inverse gives the correct result:

Assign memory addresses to social security numbers based on a hashing algorithm:

Assign each social a location, ensuring that there are no collisions:

Compute the result:

Compute the hash of a single social security number:

Simulate a particle bouncing in a noncommensurate box:

System of 12-tone equal temperament:

Notes that have a difference of 1200 cents are considered to be from the same congruence class: