# Discrete Math or modulus

1. May 18, 2009

### bphysics

1. The problem statement, all variables and given/known data

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

2. Relevant 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).

3. 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.

2. May 18, 2009

### Dick

54 is right, 52 is wrong. But your method is dubious. It looks like you are trying use a rule like (a+b)^n mod m=(a^n mod m)+(b^n mod m). That's not right. What is true is that a^n mod m=(a mod m)^n. Just use that 56 mod 55=1.

3. May 18, 2009

### bphysics

Thanks so much =D, i'll remember that.

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