Question

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

Answer 1

Answer:

Step-by-step explanation:

We have

a and b are two odd positive integers such that a & b

but we know that odd numbers are in the form of 2n+1 and 2n+3 where n is an integer.

so, a=2n+3, b=2n+1, n∈1

Given ⇒ a>b

now, According to a given question

Case I:

2a+b/2 = 2n+3+2n+1/2

=4n+4/2

​=2n+2=2(n+1)

put let m=2n+1 then,

a+b/2=2m ⇒ even number.

Case II:

a−b/2 = 2n+3−2n−1/2

​=2/2

​=1 ⇒ odd number.

Hence we can see that one is odd and the other is even.

These are required solutions.