The question is as follows:

let there be a set a1,a2,a3,...an.

If n is odd, prove that if (a1-1)(a2-2)...(an-n) **≠** 0, then the product is an even number.

From what I see, only odd number \* odd number gives an odd number, otherwise it is even. So why can't the above question be odd? Can't all the subtractions yield all odd numbers? Any help would be appreciated.