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**1. Homework Statement**

Question 1.

http://people.math.carleton.ca/~mezo/A2math1102-11.pdf

**2. Homework Equations**

r1 = a modn

r2 = b modn

r = (a+b) modn

**3. The Attempt at a Solution**

I used the division algorithm

So:

a = (q1)n + r1

b = (q2)n + r2

(a+b) = (q3)n + r

i isolated for r1 and r2 to get more equations

r1 = a - (q1)n

r2 = b - (q2)n

r = (a+b) - (q3)n

r1+r2 = (a+b) -n(q1+q2)

I then added a and b together to get the following:

a+b = r1+r2 + n(q1+q2)

After that, i`m completely lost.

This is for question 1 by the way. I've been toying around with this question for 15 hours and i still can't do anything with it. I thought i proved it before but then i realized it wasn't a proof. Please help. I'm dying.

Also another thing that i'm having trouble with is 3. I don't understand why it's worth 10 marks. All i see is me setting equation 1 and 2 equal to each other. I don't understand what's so special about that.

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