(4) This problem pertains to sums of squares and the Gaussian integers. a) Determine with justification whether or not the following integers may be written as a sum of squares. i) 12789 ii ) 14651 iii ) 42471 b) Factor fully the following elements of Z(i]. i) 2184. ii ) 1530 iii) 39 + 1042 iv ) 36 + 2i