Due Friday, October 16th

For Friday:

  • 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 F3[X]:
    1. Notice that the prime is 3!
    2. Compute (X^2+2X+1)*(X+1).
    3. Divide X^4 + X^2 + 1 by X^2 + X + 1 and determine the remainder.  Check your work afterward by multiplying out.
    4. 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).
    5. 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).
    6. Hand in your answers to the canvas dropbox.
    7. Check your answers against these solutions (only after you’ve done them all!).