# 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 iseven.

1
by yogi1

Log in to add a comment

by yogi1

Log in to add a comment

Given a and b are odd numbers

we can define b in terms of as

b = a - 2d

here a- 2d because a>b

d= any constant

( example if a = 27 and b = 21 then the d = 3 ie 2d=6 )

the difference any two odd positive number is always even .

now 1) a + b / 2

= ( a + (a - 2d ) ) /2

= (2a - 2d ) /2

=( even number ) /2

= even

2) a - b / 2

= ( a - (a - 2d ) ) / 2

= ( 2d ) /2

= d

= odd

d = 2d / 2

and d is always odd

( eg a=501 and b = 251

2d = 250

d = 125 which is odd)