Thread: Remainder and Modulus

We have to prove (a rem n) = a (mod n).

Now I know a rem n is whatever the remainder is of a/n. And for mod its usually z = a (mod n) = n / (z-a). I'm just not sure how to prove the problem above. Any suggestions because I know this is probably easy, i'm just not getting it.

Originally Posted by BlakeRobertsonMD

We have to prove (a rem n) = a (mod n).

Now I know a rem n is whatever the remainder is of a/n. And for mod its usually z = a (mod n) = n / (z-a). I'm just not sure how to prove the problem above. Any suggestions because I know this is probably easy, i'm just not getting it.

z = a (mod n) indeed means that n divides (z-a)

Now how is the remainder defined? Write a = y * n + z where 0 <= z < n.

So after writing out the defined remainder a = y*n + z

Do I try to work it out so it equals y = n/ z-a? which would represent z = a (mod n) and prove (a rem n) = a (mod n)?

You can't work out a = yn + z to equal y = n/ z-a.

Is there something else that i'm missing? is the (a rem n) = a (mod n) = y ?