Let a = 2q + 3 and b = 2q + 1 be two positive odd integers such that a > bNow, (a+b)/2=(2q+3+2q+1)/2=(4q+4)/2=2q+2=an even numberand (a−b)/2=((2q+3)−(2q−1))/2=(2q+3−2q−1)/2=2/2=1=an odd numberHence one of the two numbers (a+b)/2 and (a−b)/2 is odd and the other is even for any two positive odd integer.