Problem
COM-B1-M05-P006 Seventeen Numbers
#6
★★☆☆☆ Level 2 of 5
Prove that among any \(17\) integers, three have the same residue modulo \(8\).
If each residue class contains at most two numbers, there are at most \(16\).
There are \(8\) residue classes. If each contains at most \(2\) numbers, the total is at most \(16\), but there are \(17\). Hence some class contains at least \(3\).
Strengthened form on residues.