# Discrete Math or modulus

## Homework Statement

Find the remainder of dividing 2(562009)-3.

## Homework Equations

Let m be a positive integer. If a$$\equiv$$b (mod m) and c$$\equiv$$d (mod m), then a + c $$\equiv$$ b + d (mod m) and ac$$\equiv$$bd (mod m).

## The Attempt at a Solution

Using ac$$\equiv$$bd (mod m):

(2 mod 55)(562009mod 55) - (3 mod 55)

Using a + c $$\equiv$$ b + d (mod m)

(2 mod 55)((552009 mod 55) + (12009 mod 55)) - (3 mod 55)

(2)(0+1)-(3) = -1 OR remainder of 54

This was a problem on my math test and I got 52 as the remainder at first, but it was wrong.

Thx if you can help me.