Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Definition 1: Let 1, y E Z. Then I is divisible by y if there exists an integer k such that I = ky. Definition 2: The product of two consecutive integers is always divisible by 2. For example, k? + 3 and k² + 4 are two consecutive integers for all integers k. Hence, its product (k2 + 3)(k² + 4) is divisibe by 2. I. Prove the following statements using the indicated proof. 1.) Let I € Z. If r is odd, then (r² + 3)2021 is even. (Direct Proof)

Definition 1: Let 1, y E Z. Then I is divisible by y if there exists an integer k such that I = ky. Definition 2: The product of two consecutive integers is always divisible by 2. For example, k? + 3 and k² + 4 are two consecutive integers for all integers k. Hence, its product (k2 + 3)(k² + 4) is divisibe by 2. I. Prove the following statements using the indicated proof. 1.) Let I € Z. If r is odd, then (r² + 3)2021 is even. (Direct Proof)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
See similar textbooks
icon
Related questions
Question

If this will be factored  by 2. 

Definition 1: Let 1, y E Z. Then I is divisible by y if there exists an integer k such that I = ky. Definition 2: The product of two consecutive integers is always divisible by 2. For example, k? + 3 and k² + 4 are two consecutive integers for all integers k. Hence, its product (k2 + 3)(k² + 4) is divisibe by 2. I. Prove the following statements using the indicated proof. 1.) Let I € Z. If r is odd, then (r² + 3)2021 is even. (Direct Proof)
Transcribed Image Text:Definition 1: Let 1, y E Z. Then I is divisible by y if there exists an integer k such that I = ky. Definition 2: The product of two consecutive integers is always divisible by 2. For example, k? + 3 and k² + 4 are two consecutive integers for all integers k. Hence, its product (k2 + 3)(k² + 4) is divisibe by 2. I. Prove the following statements using the indicated proof. 1.) Let I € Z. If r is odd, then (r² + 3)2021 is even. (Direct Proof)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
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
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
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS