Let be the four digits of a four digit number
Find the maximum value of
Wouldn't it be 1000?
So, if , then we get , which is the most that can be.
Since the number must have four digits, we can't have , so it must be at least 1, and since , we have that .
So, we get and .
Actually, N=2000,3000,4000,...,9000 works also, but in all those cases we have that