We have seen that congruence modulo m is an equivalence relation on Z(all integers) for any integer m >= 1. Describe the set of equivalence classes for congruence modulo 8 - how many distinct classes are there and what are they?
What I am getting out of this is that there are 7 distinct classes and they are 1-7. But then again I am completely clueless on this modulo stuff and I've already gone to the professor with no luck on understanding it any better.
Show that addition modulo 8 is well-defined. (Use arbitrary elements from two equivalence classes [a] and [b] and how that the result is an element in [a] + [b]).
We briefly went over this in class and I again didn't understand it because of the whole modulo thing. I think it is something to do with taking two classes that are equivalent to mod 8 (which I am not sure how to figure out) and then proving that if you add them together you get whatever the question is asking.
That's just it though, I am not understanding the question nor how to find a part of what it is asking. Can anyone clarify this for me?
Help is appreciated!