(a) . Let x E Z. List all possible remainders of 7x² when divided by 3. Justify your answer. (b) [ ] Consider the following equation 7x² – 3y = 92. Prove that the equation has NO integer solutions.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 31E
icon
Related questions
Question

vA Q1

(a) .
Let x E Z. List all possible remainders of 7x2 when divided by 3. Justify your answer.
(b) [
] Consider the following equation
7x2 – 3y = 92.
Prove that the equation has NO integer solutions.
Hint: Use part (a) and the Division Algorithm Theorem.
Transcribed Image Text:(a) . Let x E Z. List all possible remainders of 7x2 when divided by 3. Justify your answer. (b) [ ] Consider the following equation 7x2 – 3y = 92. Prove that the equation has NO integer solutions. Hint: Use part (a) and the Division Algorithm Theorem.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning