Let x E Z. List all possible remainders of 10x² when divided by 3. Justify your answer. (b) [ Consider the following equation 10x? – 3y = 95 Prove that the equation has NO integer solutions. Hint: Use part (a) and the Division Algorithm Theorem.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 31E
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(a) , Let x E Z. List all possible remainders of 10x² when divided by 3. Justify your answer.
(b) [ Consider the following equation
10x² – 3y = 95
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 10x² when divided by 3. Justify your answer. (b) [ Consider the following equation 10x² – 3y = 95 Prove that the equation has NO integer solutions. Hint: Use part (a) and the Division Algorithm Theorem.
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