Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º, 7 = 2² +2+1. Hint: use strong induction. You may use the fact that for all positive integer n, there exists a non-negative integer m such that 2m ≤ n < 2m+¹, i.e. 2m is the largest power of 2 no greater than n.

Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º, 7 = 2² +2+1. Hint: use strong induction. You may use the fact that for all positive integer n, there exists a non-negative integer m such that 2m ≤ n < 2m+¹, i.e. 2m is the largest power of 2 no greater than n.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.6: Congruence Classes
Problem 20E
See similar textbooks
icon
Related questions
Question
Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º, 7 = 2² +2+1. Hint: use strong induction. You may use the fact that for all positive integer n, there exists a non-negative integer m such that 2m ≤ n < 2m+1, i.e. 2m is the largest power of 2 no greater than n.
Transcribed Image Text:Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º, 7 = 2² +2+1. Hint: use strong induction. You may use the fact that for all positive integer n, there exists a non-negative integer m such that 2m ≤ n < 2m+1, i.e. 2m is the largest power of 2 no greater than n.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
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
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS