Question

please solve question no. 1

Answer 1

Let a be 2n + k and b be 2n + 1 (since a> b, k>1 and k is odd such that a and b are odd, n ∈ N)

(a+b)/2 = (4*n + k+1)/2 = 2*n + (k+1)/2

while (a-b)/2 = (k-1)/2  

So now the question simplifies to find the nature of (k+1)/2 and (k-1)/2

consider k=2*m+1 (since k>1 ; m>0)

now (k+1)/2 = m+1 while (k-1)/2 = m

Depending on value of m; one of the numbers - m and m+1 will be odd while other is even which implies one of the number (a+b)/2 and (a-b)/2 is odd while other is even