For i = 1, 2, ..., n, let Ai, Bi, Ci ( (i and set E = A1 ×...×, × An, F = B1 ×...× Bn, G = C1 ×...× Cn. Suppose that E, F, and G are all ( ( and that E = F + G. Then show that there exists a j with 1 ≤ j ≤ n such that A j = B j + C j while Ai = Bi = Ci for all i ( j.