MathDB

If we add

1996

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\cdot k

1997\cdot k

no carry arises during the whole calculation?

Problem Statement