Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c ≤ 18 such that: 12. (a − b) ≡ c mod 19 13. (7a + 3b) ≡ c mod 19 14. (2a2 + 3b2) ≡ c mod 19
Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c ≤ 18 such that: 12. (a − b) ≡ c mod 19 13. (7a + 3b) ≡ c mod 19 14. (2a2 + 3b2) ≡ c mod 19
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 57E
Related questions
Question
Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c ≤ 18 such that:
12. (a − b) ≡ c mod 19
13. (7a + 3b) ≡ c mod 19
14. (2a2 + 3b2) ≡ c mod 19
15. (a3 + 4b3) ≡ c mod 19
please show your solutions :)
I've already seen other answers to the problems but I'm unsure if that's correct pls help
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,