Question: QUESTION THREE(20 MARKS) a) Use mathematical induction to prove that 57 divide n=0 7n+2+8n+1 (6 marks) b) Let a=195 and b=968. Use the division

QUESTION THREE(20 MARKS) a) Use mathematical induction to prove that 57 divide

QUESTION THREE(20 MARKS) a) Use mathematical induction to prove that 57 divide n=0 7n+2+8n+1 (6 marks) b) Let a=195 and b=968. Use the division algorithm to find the gcd(a,b) and therefore find integers m and n such that d-am +bn c) Consider the third order homogeneous recurrence relation a, = 6a,-1 i. ii. Find the general solution Find the initial solution given a, = 3, a = 4,a = 12 (6 marks) +8a-3 -12a-2 (4 marks) (4 marks)

Step by Step Solution

★★★★★

3.40 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The detailed answer for the above question is provided below a We can use mathematical induction to prove that 57 divides 7n2 82n1 for all negative in... 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!

Arrow Air is a regional East Coast airline that has collected data for the percentage available seats occupied on its flights for four quarters(1) JanuaryMarch, (2) AprilJune, (3) JulySeptember, and...

Use mathematical induction to prove that 43 divides 6n+1 + 72n1 for every positive integer n.

Use mathematical induction to prove that 64 divides 32n+2 + 56n + 55 for every positive integer n.

Use mathematical induction to prove that breadth-first search visits vertices in order of their level in the resulting spanning tree.

Trusted software could then be run on the workstation. Discuss the advisability of this approach to workstation design. (10 marks) b) Explain how distributed inter-process communication (IPC) is...

Source: https://businesstech.co.za/news/business/622829/one-of-south-africas-biggest-retailershas-major-plans-to-create-jobs-and-open-new-stores please see link above to answer following questions...

Suppose P and Q are polynomials and is a positive integer. Use mathematical induction to prove that the nth derivative of the rational function f(x) = P(x) / Q(x) can be written as a rational...

(a) Show that ex > 1 + x for x > 0. (b) Deduce that ex > 1 + x ½ x2 for x > 0. (c) Use mathematical induction to prove that for x > 0 and any positive integer n, e*>1+x++ 2! n!

A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble is then placed on the first one. This process is continued until chambers, including the sphere, are...

Use Mathematical Induction to prove that if the set S has n elements, then P(S) has 2n elements.

Use mathematical induction to prove that for n > 2, ..+ an-12"-1 +1") det(C, A1) = (-1)"(o + ajd + = (-1)" p(2)

What are fixed spots, preemptible spots, and floating spots in radio advertising?

Refer to the information for Fly High Airlines above. During the past year, the high and low use of three different resources for Fly High Airlines occurred in July and April. The resources are...

Where are the opportunities in this market?" is one of the ten critical questions you should ask about an industry. a . True b . False

Given the following data for the titration of oxalate (C,0,2) ion with zinc ion, write the titration reaction, and calculate the following: Vor = 30.50 ml (Ox?] = 0.1350 M (Zn"] = 0.200 M Ksp = 2.73...

Many proteases are produced as longer precursors, they are activated randomly, and the likeliness of activation increases when they reach the location of the action. True/false

Sienna's Health and Fitness established a sinking fund to purchase a 10-acre parcel of land for their new headquarters and Distribution center on a $5,000,000 loan due in 8 years. To meet this...

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...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

ANSI-SPARC6 Programming Language Compilation Write notes on each of the following topics: (a) the implementation of labels and jumps in a recursive, block structured programming language [7 marks]...

"Fortran, Algol and Lisp invented most programming language concepts 50 years ago; adding the concept of object-orientation suffices to explain all programming languages to date". To what extent is...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

s sf Define the terms opaque type and concrete type. [5 marks] The following is a shortened version of one of the definition modules described in the Modula-2 user manual: Provide a suitable...