Homework Assignment #3

Show all work. i.e., justify your answers.

1.9 in the textbook (be sure to complete both proofs! – each is worth 3 points)

• “justify” means prove using a two column proof: one column for statements and one column for reasons.

1.18 in the textbook

1.20 in the textbook (four sub-problems – each is worth 3 points)

• Use the Extended Euclid method on two of the sub-problems
• Any method (including Extended Euclid) is welcome for the other two sub-problems
• If you get a negative result for the multiplicative inverse, then add the modulus until you obtain a positive value between 0 and the modulus (exclusive of 0 and the modulus).

In order to be successful on the problems using the Extended Euclid algorithm, please be sure to consult the posted example. It is a walk-through of the recursive algorithm: Worked Example