Homework 3
MA 522 Fall 2008
1. (20 points) Write a pseudo-code for the division with remainder algorithm over Z
2. (40 points) Textbook, page 40/ 2.10 (i) and (iii)
3. Your answers for this problem should be submitted as a MAPLE worksheet (by email),
including your implementation and the output of the examples in part (b).
(a) (20 points) Implement in MAPLE the Extended Euclidean Algorithm for Zp[x], i.e. for
univariate polynomials over the field Zp={0,1, . . . , p −1}where pis an arbitrary prime
number. Use MAPLE’s datastructure for polynomials and its modular arithmetics.
(b) (20 points) Textbook, page 59/ 3.14
4. Extra credit problem (20 points) Textbook, page 60/ 3.25 (ii) and (iii)
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