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## Homework Statement

Find the remainder of dividing 2(56

^{2009})-3.

## Homework Equations

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

## The Attempt at a Solution

Using ac[tex]\equiv[/tex]bd (mod m):

(2 mod 55)(56

^{2009}mod 55) - (3 mod 55)

Using a + c [tex]\equiv[/tex] b + d (mod m)

(2 mod 55)((55

^{2009}mod 55) + (1

^{2009}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.