Problem
COM-B1-M05-P009 Difference Divisible by \(100\)
#9
★★☆☆☆ Level 2 of 5
Prove that among any \(101\) integers, two have a difference divisible by \(100\).
Residues modulo \(100\).
There are \(100\) residues modulo \(100\). Among \(101\) integers, two have the same residue, so their difference is divisible by \(100\).
Direct residue problem.