Question: Use weak induction to prove that for n N , 7 n+2 + 8 2n+1 is divisible by 57. Base Case: 7 3 + 8

Use weak induction to prove that for n N , 7n+2 + 82n+1 is divisible by 57.

Base Case: 73 + 83 = 343 + 512 = 855 = 15 * 57

Induction Hypothesis: 7n+2 + 82n+1 is divisible by 57

Induction Step:

Prove 7(n+1)+2 + 82(n+1)+1 is divisible by 57

7(n+1)+2 + 82(n+1)+1 = 7n+3 + 82n+3

= 7(7n+2) + 8*8(82n+1)

I'm stuck here...can you help?

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 Mathematics Questions!

Q:

Data gistrun sending inside a pack fills in as conventional allowing subordinate rules to execute on progressive clock cycles. Correspondence between gatherings conventionally causes a surprising...

Q:

Exercise 1: Express the following in summation notation. (a) 1 + 20400 8, 000+.... Express the following in summation notation and use induction to prove for n (a natural number) 1. 1+3+5+ (2n-1) n2...

Q:

9/14/10 12:27 PM Page 321 Chapter dug84356_ch05a.qxd 5 Factoring The sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. Today,...

Q:

MATHEMATICAL INDUCTION CJ Cambre Jr. [COMPANY NAME] [Company address] Carlos Cambre Professor Nickerson MAT 403 December 9, 2016 Mathematical Induction Pierre de Fermat really knew he used...

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

Q:

\f\f\f\f\f\f\f\f\f\fSequences, Mathematical Induction and Recursion 1 5.1 Sequences 2 Sequences Sequences represent ordered lists of elements. A sequence is defined as a function from a subset of N...

Q:

1. Set up an induction proof, prove the base case and set up the inductive step (say what the induction hypothesis would be, and what would need to be proved in the inductive step). Just set up the...

Q:

# 5: Fourier Interpolant and DFT 1 The Discrete Fourier Transform (DFT) of a periodic array fj , for j = 0, 1, . . . , N 1 (corresponding to data at equally spaced points, starting at the left end...

Q:

# 5: Fourier Interpolant and DFT 1 The Discrete Fourier Transform (DFT) of a periodic array fj , for j = 0, 1, . . . , N 1 (corresponding to data at equally spaced points, starting at the left end...

Q:

Why do we need special legislation designed to control foreign libel claims against U.S. citizens? As mentioned earlier, U.S. plaintiffs sometimes engage in forum shopping by trying to have their...

Q:

SOLVED PROBLEMS 19.1 The following information is available for Avinash Metals. Net operating income 40 million Interest on debt 10 million Cost of equity Cost of debt 18 percent 12 percent (a) What...

Q:

A couple has just purchased a home for $ 4 3 5 , 9 0 0 . 0 0 . They will pay 2 0 % down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 6 . 9 6 %...

Q:

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.