if a and b are odd then a + b is even Let a and b be positive odd integers of the form: a = 2n + 1 b = 2m + 1 a + b = 2n + 1 + 2m + 1 a + b = 2n + 2m + 1 + 1 Combing like terms, we get: a + b = 2n + 2m + 2 a + b = 2(n + m) + 2 Let k = n + m a + b = 2k + 2 Therefore a + b is even