Problem
COM-B1-M11-P013 Nine Remainders
#13
★★★☆☆ Level 3 of 5
Prove that among any \(10\) integers, two have a difference divisible by \(9\).
Compare \(10\) numbers and \(9\) residues.
There are \(9\) residues modulo \(9\). Among \(10\) numbers, two have the same residue. Their difference is divisible by \(9\).
Small strengthening of the standard task.