Here is the link to the Problem and Solution of December cookoff YVNUM. Ex. string 921, modulo number = 103 asked 24 Dec '18, 18:51

We first try to represent the number as sum of several numbers. Now, as the numbers become large, we take the modulo of the component numbers instead of the digits. So, to find modulo of (921219192), we break it as a = 921 * 10^6 So,921219192 = a + b + c So, now the answer is (a%103+ b%103 + c%103)%103. And I don't think that just taking modulo of each cyclic shift and then concatenating it would work. answered 24 Dec '18, 19:01
