- #1
PolyFX
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Homework Statement
Solve 3x + 50 = 11 in F53
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 - 2Now 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