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## Homework Statement

Solve 3x + 50 = 11 in F

_{53}

## Homework Equations

Extended Euclidean Algorithm

## The Attempt at a Solution

To find 3

^{-1}mod 53 using the euclidean algorithm:

gcd(53,3)

1)53/3 = 17 + 2R

53 = 17 * 3 + 2

2 = 53 - 17 * 3

3/2 = 1 + 1R

3 = 1 * 2 + 1

1 = 3 - 1 * 2 = 3 - 2

Now going from reverse;

1 = 3 - (53 - 17 * 3)

= 3 - 53 + 17 * 3

= 18*3 - 53

3

^{-1}= 18 mod 53

3x + 50 = 11

3x = 11 - 50 mod53 ==> 3x = -39 mod 53

3x = 14 mod 53

I'm stuck after this step. How do I solve for x?

-Thanks