MathDB
residue classes, existence where [a] is class mod mn

Source: VTRMC 2011 P4

May 14, 2021
number theorySets

Problem Statement

Let m,nm,n be positive integers and let [a][a] denote the residue class(modmn)\pmod{mn} of the integer aa (thus {[r]∣r is an integer}\{[r]|r\text{ is an integer}\} has exactly mnmn elements). Suppose the set {[ar]∣r is an integer}\{[ar]|r\text{ is an integer}\} has exactly mm elements. Prove that there is a positive integer qq such that qq is coprime to mnmn and [nq]=[a][nq]=[a].
Back to ProblemsView on AoPS