CS 3333 Mathematical Foundations    Spring '12

Solve the following problems from the textbook [KR]. For each problem, show the intermediate steps and the final answer.

Division and Modular Arithmetic, Pages 244 --245: 3, 5, 6, 10 c, d & e, 14 c & d, 17 (prove using the division algorithm that n = qk +r, 0 <= r < k), 18, 20 c & d, 26, 34, 36, 40.

Primes, GCDs and LCMs, Pages 272--274: 2, 3, 5, 12, 14 (find integers < 50 that are relatively prime to 50), 17, 18 (for part b: list all positive divisors; do not have to prove), 20 b & d, 24 c & f, 26 c & f, 28, 30, 32 e & f, 35, 40 a & d, 50, 52 (Hint: give a counterexample).

Applications of congruences: Page 292: 2 c & d, 6 (use seed 4).
Cryptography: Pages 304: 2 c, 4 c.
 

Submit a legible hard copy of your answers in the classroom by 4 pm on the date specified.

Rajendra V. Boppana
Mail: CS Department, UT San Antonio, San Antonio TX 78249, USA
Phone: 210-458-5692  Fax: 210-458-4437   Email: boppana[at]cs.utsa.edu