well E was my first answer.... Let 's me post the official explanation
I quote " :
note that for the two consecutive integers the larger must be 1 more than the smaller .that st1 alone is sufficient can probably be seen most easily by considering particular values of m and n .
for example if m =4 Then n=3 or 5 since m and n are consecutive
then m -1= 3 AND n +1 =4 or 6 since m-1 and n+ 1 are consecutive, m bigger than n .
more generally since m and n are consecutive either m= n+1
but if n=m+1. then n+1=m+2, which is 3 more than m-1 , contradicting the fact that m-1 and n+1 are consecutive integer .
THus m=n+1 OR m bigger than n
when there is a will there is a way