- Prove the following: a) A positive integer n is divisible by 5 if and only if its last digit is 0 or 5. b) If x and y are rational numbers and y = 0, then xy is also rational. c) Let n be any integer. Prove by cases that n3 - n is evenly divisible by 3. d) Let n 70. If 2n4 +n + 5 is odd, then n is even. e) Suppose 12x + 3y = 254, for real numbers x and y. Then either x ory (or both) is not an integer. f) n! > 3 for n > 7. 1 + 3 + 32 +33 + ... + 3" = (31+1 1) / 2 Vn20 h) For distinct positive real numbers x and y, 0.5 (x + y) > (xy)0.5