I need to explain how positive and negative integers can be combined under the operations of addition and multiplication using mod 5. I need to give examples of how I could use this in addition using positive numbers and then negative numbers. I also need to describe how to use this in multiplication using positive and then negative numbers.
I have read so many different materials on mod and am still having incredible difficulty figuring this out.
First you can make every integers including the negative one to be 0,1,2,3, or 4 modulo 5.
since -63=-65+2=5(-13)+2, then -63=2 modulo 5.
Then one you translate every integer into either 0,1,2,3 or 4 then addition and multiplication are basically addition and multiplication involving 0,1,2,3,4 only.