If a and b are two positive odd integers prive that one out of a+b÷2 and a-b÷2 is odd and other is even.
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let a = 2n+1 and b = 2m+1
c = n+m+1 ; d = n-m
case if d is odd; means one of n or m is odd which will render c as even
if d is even both n,m are odd or even and hence c becomes odd.
hence if d is odd c is even else if d is even c is odd
that means one of d and c is even and other is odd
c = n+m+1 ; d = n-m
case if d is odd; means one of n or m is odd which will render c as even
if d is even both n,m are odd or even and hence c becomes odd.
hence if d is odd c is even else if d is even c is odd
that means one of d and c is even and other is odd
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