To Know: The next module assessment (for RSA, primality testing, euclidean algorithm, factoring etc) will go up on Thur or Fri and be due next Friday.

The last assessment is almost all graded, you may get it back tomorrow or on the weekend.

To Do: Practice working in F_{3}[X]:

Notice that the prime is 3!

Compute (X^2+2X+1)*(X+1).

Divide X^4 + X^2 + 1 by X^2 + X + 1 and determine the remainder. Check your work afterward by multiplying out.

Determine the gcd of X^4 + X + 1 and X^2 + 1. You will likely get a result of “2”. Keep in mind that 2*2 = 1, so this really means they are “coprime” (we can discuss this in class a bit).

Solve the Diophantine equation s(X^4+X+1)+t(X^2+1) = 1. Hint: If you got “2” as the gcd, then solve the (equation=2) first, then use 2*2=1 to figure out how to get the solutions to the (equation=1).

Hand in your answers to the canvas dropbox.

Check your answers against these solutions (only after you’ve done them all!).