# example of pigeonhole principle

A example.

###### Theorem.

For any set of $\mathrm{8}$ integers, there exist at least two of them
whose difference^{} is divisible by $\mathrm{7}$.

###### Proof.

The residue classes^{} modulo $7$ are $0,1,2,3,4,5,6$.
We have seven and eight integers. So it must be the case that 2 integers fall on the same
residue class, and therefore their difference will be divisible by $7$.
∎

Title | example of pigeonhole principle^{} |
---|---|

Canonical name | ExampleOfPigeonholePrinciple |

Date of creation | 2013-03-22 12:41:32 |

Last modified on | 2013-03-22 12:41:32 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 8 |

Author | Mathprof (13753) |

Entry type | Example |

Classification | msc 05-00 |