1. Compute without a calculator: (a) 59 + 63 mod 13 (b) 15 * 29 mod 13 (c) 2 * 29 mod 13 (d) –10 * 29 mod 13 (e) (23 * 100098 + 7) * 29 mod 13 2. Compute the gcd of the number below using 1) factorization, 2) using Euclid's division algo- rithm: (a) gcd(24, 15) (b) ged(172, 20) (c) gcd(54, 21) 3. Using the reverse of Euclid's division algorithm compute: (a) Find integers x, y such that 24x + 15y = 3 (b) Find integers x, y such that 172x + 20y = 1000 (c) Find integers x, y such that 23x + 17y =1 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 (c) mod 7

1. Compute without a calculator: (a) 59 + 63 mod 13 (b) 15 * 29 mod 13 (c) 2 * 29 mod 13 (d) –10 * 29 mod 13 (e) (23 * 100098 + 7) * 29 mod 13 2. Compute the gcd of the number below using 1) factorization, 2) using Euclid's division algo- rithm: (a) gcd(24, 15) (b) ged(172, 20) (c) gcd(54, 21) 3. Using the reverse of Euclid's division algorithm compute: (a) Find integers x, y such that 24x + 15y = 3 (b) Find integers x, y such that 172x + 20y = 1000 (c) Find integers x, y such that 23x + 17y =1 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 (c) mod 7

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 12E

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