17. Prove that the product of two integers, one of the form 3/ + 2 and the other of the form 3/2 + 2 , where kj and ky aro intogers, is of the form 3/, | 1 for some intogor ka . Using Direct Proof: Let m = 3k + 2 Let n = 3k, + 2 If m = 3k, + 2 and n = 3k, + 2, then, m*n = (3k, + 2) (3k, + 2) = 9k.k, + 6k, + 6k, + 4 = 3(3k,k, + 2k, + 2k,) + 4 = 3(3k,k, + 2k, + 2k, + 1) + 1 QED