example of pigeonhole principle

A example.


For any set of 8 integers, there exist at least two of them whose differencePlanetmathPlanetmath is divisible by 7.


The residue classesMathworldPlanetmath 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 principleMathworldPlanetmath
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