A number theory problem by Satwik Murarka

@Satwik Murarka I think you will have to show that by all the three digit number divisors it gives the same remainder $97$ .

As an example , suppose in the question there were numbers $4143 , 3143$

Then we would be searching for numbers that divide $1000$ , so it could be $100 , 200 , 125 , 500$ and the remainders different in different cases. Like by $100$ it is 43 , by $200$ it is $143$ and so on.