Definitions: An integer n is even if and only if there exists an integer k such that n = 2k. An integer n is odd if and only if there exists an integer k such that n = 2k + 1. Two integers have the same parity when they are both even or when they are both odd. Two integers have opposite parity when one is even and the other one is odd. An integer n is divisible by an integer d with d0, denoted din, if and only if there exists an integer k such that n = dk. A real number r is rational if and only if there exist integers a and b with b 0 such that r = a/b. For any real number x, the absolute value of x, denoted lxl, is defined as follows: Ixl - / x if x 20 1x1 = -x if x