Question: Prove that any positive integer can be written as a sum of distinct powers of 2

Prove that any positive integer can be written as a sum

Prove that any positive integer can be written as a sum of distinct powers of 2

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

3. Strong Induction (11 points) (1) (6 points) Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 7-cent stamps. The Induction and Recursion parts of this...

Q:

3. Strong Induction (11 points) (1) (6 points) Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 7-cent stamps. The Induction and Recursion parts of this...

Q:

(2) (5 points) Use strong induction to show that every positive integer can be written as a sum of distinct powers of two (i.e., 2- 1,21 -2,22 4,23 8,21-16....) For example: 19 16+2+1-24 21 20 Hint:...

Q:

Problem. Write positive integer n as a sum of at most 4 squares. Mathematicians can prove that a positive integer can be written as the sum of at most 4 squares. That is, if n is a positive integer,...

Q:

Question 1 .Use strong induction to show that every positive integern can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers20=1,21=2,22=4, and so on. (For...

Q:

show work. use a pen and paper. Mathematical Induction and Proofs 1. [1 point] Show that a21 is divisible by 8 for all odd a 's. 2. [1 point] Show that every positive integer can be written as a sum...

Q:

Mathematical Induction and Proofs 1. [1 point] Show that a21 is divisible by 8 for all odd a 's. 2. [1 point] Show that every positive integer can be written as a sum of some powers of 2 . 3. [1...

Q:

PLEASE HELP ME ANSWER THESE QUESTIONS AND I DONT NEED ANY EXPLANATION. 1. Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a...

Q:

1. Prove that P(A)=2A for any set A. 2. For which positive integers are the following propositional functions true? 1. P(1) is true. For all positive integers n,P(n)P(n+1). 2. P(1) is true. For all...

Q:

Every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 -1,21 -2, 22-4, and so on. If proving this with strong induction, what...

Q:

Recycling trash, reducing waste, and reusing materials are eco-actions that will help the environment. According to a USA Today snapshot (Exercise 6.45), 78% of respondents list recycling as the...

Q:

Consider the graph with vertex set {A, B, C, D, E} and edge list AD, AE, BC, BD, DD, DE. (10 points) 1. Draw the graph. 2. List all the vertices adjacent to D. 3. List all the edges adjacent to BD....

Q:

Earnings per share: Multiple Choice 0 : 4 0 : 1 4 must increase at the same rate as the net income. is defined as the addition to retained earnings divided by the number of shares outstanding. will...

Q:

What is the performance of Dollar Tree in year 2 0 2 3 and 2 0 2 2 in financial performance?

Q:

1 Is there a relationship between cultural values in specific countries (e.g. collectivism, power distance, instrumentalism, humanism) and the way (indigenous) organizations respond to changes in...

Q:

4 For managers to operate effectively they need to learn to think more strategically and outside ordinary line responsibilities of operational fire fighting. This type of project work can facilitate...

Q:

3 As there is a continuing need for this type of working across borders and cultures, thought should be given to common decision premises based on the managing of different cultures, value systems,...