Since so but if from the unit digit of we conclude that is odd but it is the multiple of which should be even . Therefore ,

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 :

we have

When

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 ...