Problem
COM-B1-M12-P011 Set 3. Remainders
#11
★★☆☆☆ Level 2 of 5
Prove that among any \(9\) integers, two have the same remainder modulo \(8\).
There are only \(8\) residues.
There are \(8\) residues modulo \(8\), and \(9\) numbers. By pigeonhole, two numbers have the same residue.
Residue form of pigeonhole.