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[parent] example of pigeonhole principle (Example)

A simple example.

Theorem 1   For any set of $8$ integers, there exist at least two of them whose difference is divisible by $7$ .


\begin{proof} The \htmladdnormallink{residue classes}{http://planetmath.org/ency... ...class, and therefore their difference will be divisible by <SPAN class=$7$ . \end{proof}">



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Cross-references: residue classes, divisible, difference, integers

This is version 5 of example of pigeonhole principle, born on 2002-05-30, modified 2007-04-16.
Object id is 2972, canonical name is ExampleOfPigeonholePrinciple.
Accessed 5600 times total.

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AMS MSC: 05-00 (Combinatorics :: General reference works )
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