Question

If a and b are two odd positive integers such that a > b, then prove that one of the two numbers (a+b)/2 and (a-b)/2 is odd and the other is even.

Answer 1

Let a = 2q + 3 and b = 2q + 1 be two positive odd integers such that a > b

Hence 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​