In the middle of 2023 i.e. between 20 and 23 enter
a number such that the new number will be a multiple of 2023.

a. What is the smallest number to fulfill the above requirement?

b. What if the number to be inserted should consist of the same digit repeated n times? Please provide a solution with lowest n.

c. In case no solution exists for (b) or it needs too much time, solve for 23, inserting a string of numbers between 2 and 3 so that the resulting number will be divisible by 23.