Consider the unit digit after multiplying a number among by , we have already known it is
we have but is impossible because we conclude
Then consider the actual values of these number :
When it is impossible , so is the unique solution .
The required number is
is an indeterminated equation , any number may be the solution of provided will be an integer :
because is an integer , must be a positive odd , but if is very large which makes to be greater than , we cannot construct a number with a digit ...