Let m1, m2,…, mk be pairwise relatively prime positive integers. Let M = m1m2··· mk and Mj...

Let m1, m2,…, mk be pairwise relatively prime positive integers. Let M = m1m2··· mk and Mj = M/mj for j = 1, 2,…, k. Show that

runs through a complete system of residues modulo M when a1. a2, …, ak run through complete systems of residues modulo m1,m2,…, mk respectively.