It is clear that there are an n number of unique sets of Z_n but is there a way to calculate [a]*[b] without counting the final value of a*b and finding where that lies mod n?
It’s very interesting that everywhere we look we can always find some sort of pattern. Arithmetic is valuable not only with integers or any number but also with sets. Modular arithmetic has many possibilities of use. Computer programming uses something similar often when defining arrays and so forth.