# Thread: Number Theory. Finding the samllest nonnegative value of m.

1. ## Number Theory. Finding the samllest nonnegative value of m.

Hi all,

will anyone advice me how to solve this question?

Q: Consider the group G= (Z, +), H= (7Z, +).
Then H is normal in G and G/H is the factor group.
If (3+7H) + (4+7H) = m+7H
What is the smallest nonnegative value of m?

WeiJing

2. ## Re: Number Theory. Finding the samllest nonnegative value of m.

Hey weijing85.

Since these are integer groups can you use use congruence equations and number theory to find m? What does your lecturer expect in terms of finding the solution?

3. ## Re: Number Theory. Finding the samllest nonnegative value of m.

It was an assignment question. I don't understand at all (

4. ## Re: Number Theory. Finding the samllest nonnegative value of m.

What have you covered in class?

5. ## Re: Number Theory. Finding the samllest nonnegative value of m.

(3+7H) + (4+7H) = m+7H
The answer is 0. i got it right (:

My working is 3+4 (Mod7) = 7 (Mod 7) = 0 (Mod 7) (: