Prove the followingg statement: let a, b, c, m, n e z, where m 2 2 and n 2 2. if a b (mod m) and a c (mod n), then b c (mod d), where d = gcd(m, n). proof: for some n e z for some x e z. since a c (mod n), it follows that b (mod m), it follows that since a hence b-c= and since d gcd(m, n), it follows that for some e z and for some e z. therefore, b - c = | thus and so b c (mod d). since rx- sy e z, q. e.d