If we add 1996 to 1997, we first add the unit digits 6 and 7. Obtaining 13, we write down 3 and “carry” 1 to the next column. Thus we make a carry. Continuing, we see that we are to make three carries in total.Does there exist a positive integer k such that adding 1996⋅k to 1997⋅k no carry arises during the whole calculation? number theory proposednumber theory