Problem #PRU-60732

Problems Algebra and arithmetic 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 \(n\).