Question: III. Prove by induction the following problems:4. 52n+1 . 2n+2 + 3n+2 . 22n+1 is divisible by 19 for any positive integer n

III. Prove by induction the following problems:4. 52n+1 . 2n+2 + 3n+2 . 22n+1 is divisible by 19 for any positive integer n

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Problem Statement Prove that the expression 5 2 n 1 2 n 2 3 n 2 2 2 n 1 52n1 cdot 2n2 3n2 cdot 22n1 52n12n23n222n1 is divisible by 19 for any positive integer n n n Step 1 Base Case Lets test the expr... View full answer

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 Mathematics Questions!

Summit LLC operates with monthly accounting periods. All of the company's accounting work is completed through the end of April, and its ledgers show April 30 balances. Terms for all credit sales are...

1.16 Express the following in partial fraction form: (a) 2x' - 5x + 1 ( b ) x' +x - - 2x - x2 + x- 1.17 Rearrange the following functions in partial fraction form: x - 6 ( b ) x3 + 3x3 + x+ 19 (a) x3...

Could I get help for these please? Question 8 ? (a) The numbers p, q and s are fixed and positive. Also p > 1, q > 1 and P= q q- 1 i. What positive value of t minimises the expression 2 f (t) = + p -...

Kindly explain these attachments. QUESTION 3 Throughout this question X], Xys ..., Xmy ... will be a sequence of random variables that are defined on the same sample space !. (a) Explain what is...

QUESTION 3 Throughout this question X], Xys ..., Xmy ... will be a sequence of random variables that are defined on the same sample space !. (a) Explain what is meant by each of the following,...

Hello could someone help explain how to do these questions with working? 8 (ii) for the first and 8 (a) (iii) (iv) for the second. Question 8 ? (a) The numbers p, q and s are fixed and positive. Also...

Hello, could someone please help explain how to do parts iii and iv? Thanks Question 8 ? (a) The numbers p, q and s are fixed and positive. Also p > 1, q > 1 and P= q q- 1 i. What positive value of t...

Exercise 1. Let (N, succ) be a realization of the natural numbers with successor function succ. We define addition of the numbers 0 and 1 := succ(0) by setting n +0 :=n, n + 1 := succ(n), NEN. i)...

3. Consider the following recursive algorithm: Preconditions: A is an array of integers. f and are integers such that Osfs (e- f +1)/2: 12 return r 13 eturn maj(A, m +1,e) (a) Let T(n) denote the...

Let L be the well-known standard language of propositional logic. Now we define the language LRP of propositional formulas in Reverse Polish notation, as follows: i Each propositional atom p; is a...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

For all random variables X and Y and all constants a, b, c, and d, show that Cov(aX + b, cY + d) = ac Cov(X, Y ).

May has a goal to buy a house. She needs to save $20,000 for the down payment. 1. She has $10,000 in an account that is earning 5%, posted annually. Will she have enough in 5 years? FV FV Rate FV 2....

The business uses a hybrid business model to generate revenue by working with reputable organizations that pay fees for greater access to uncharted territory. At the same time, the corporation...

The 4-in.-radius wheel weighs 6 lb and turns about its y-axis with an angular velocity p = 40 rad/sec in the direction shown. Simultaneously, the fork rotates about its x-axis shaft with an angular...

Selected accounts and related amounts for Druid hills Co. for the fiscal year ended May 31, 20Y8, are presented in Problem 6-5A. Instructions 1. Prepare a single-step income statement in the format...

An accountant prepared the following post-closing trial balance: Prepare a corrected post-closing trial balance. Assume that all accounts have normal balances and that the amounts shown are correct....

Nestls financial statements are presented in Appendix B. Financial statements for Delfi Limited are presented in Appendix C. Instructions a. Based on the information contained in the 2016 financial...

If you speak via radio from Earth to an astronaut on the Moon, how long is it before you can receive a reply?

eBook Problem Walk Through The Stewart Company has $1,690,000 in current assets and 5642,200 in current liabilities. Its initial inventory level is $422.500, and it will raise funds as additional...

1. From what Ms. Taylor says in the video, does The Weather Channel really use a performance management process? Why do you conclude that?pg 87

3. How would you reduce the anxiety and stress of an appraisal, based on what you read in this chapter?pg 87

3. Explain in detail how to establish a market-competitive pay plan.pg 87