Exercise 3.6.3 Assume gcd(m, n) = 1. Define f : Z ->Zm ⊕ Zn by f (x) = (x + mZ, x + nZ) and show that f(x + y) =f (x) + f (y). Then show that, as additive groups, Zm ⊕ Zn and Zmn are isomorphic - using the first isomorphism theorem from the preceding section.