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## Homework Statement

Suppose a, b, n are integers with n >/= 2

Prove that:

(a + b) mod n = ((a mod n) + (b mod n)) mod n

## Homework Equations

Modular arithmetic rules.

## The Attempt at a Solution

r1 = a(modn)

=> a = q1n + r1

r2 = bmodn

=> b = q2n + r2

r1 + r2 = a - q1n + b - q2n

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

Here is where I have no idea where to go. :S