Problem
COM-B1-M05-P004 Residues Modulo \(n\)
#4
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Prove that among any \(n+1\) integers, two have a difference divisible by \(n\).
Two numbers with the same residue give the required difference.
There are \(n\) residues modulo \(n\). Among \(n+1\) numbers, two have the same residue. Their difference is divisible by \(n\).
Key residue template.