The application of basic arithmetic to finite systems of whole numbers.

In the system modulo

*n*or a restricted system of whole numbers less than*n*, we use the numbers 0, 1, 2, 3, 4, …, (*n*– 1).The arithmetic operations defined in this system are the same as those in basic arithmetic, except that the numbers used cannot be greater than (*n* – 1). When a result should be greater than (*n* – 1), we divide this result by n and we use the remainder of this division as the result of the operation.

### Example

Here is a multiplication table of the numbers in the set {0, 1, 2, 3, 4} in arithmetic modulo 5:

× |
0 | 1 | 2 | 3 | 4 |

0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 1 | 2 | 3 | 4 |

2 | 0 | 2 | 4 | 1 | 3 |

3 | 0 | 3 | 1 | 3 | 2 |

4 | 0 | 4 | 3 | 2 | 1 |