example of pigeonhole principle
A example.
Theorem.
For any set of integers, there exist at least two of them
whose difference is divisible by .
Proof.
The residue classes modulo are .
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 .
∎
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 |