Problem #PRU-60732

Problems Number Theory Divisibility Division with remainders. Arithmetic of remainders Arithmetic of remainders Methods Pigeonhole principle Pigeonhole principle (other)
 12–15  3.0

Problem

Prove that any \(n\) numbers \(x_1,\dots , x_n\) that are not pairwise congruent modulo \(n\), represent a complete system of residues, modulo \(n\).