Let а, b be positive coprime integers. a) Show that {0, a, 2a, . , (b – 1)a} forms a complete residue system modulo b. b) If n > ab, show that n can be written as a positive linear combination of a and b, i.e. there exist positive integers x, y such that n = ax +by.
Let а, b be positive coprime integers. a) Show that {0, a, 2a, . , (b – 1)a} forms a complete residue system modulo b. b) If n > ab, show that n can be written as a positive linear combination of a and b, i.e. there exist positive integers x, y such that n = ax +by.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 12E: Let A be a set of integers closed under subtraction. a. Prove that if A is nonempty, then 0 is in A....
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning