Question: 4. (6 marks) Prove that there do not exist two positive integers x and y such that 2-4y2 14. Additional information: you have all known

4. (6 marks) Prove that there do not exist two positive

4. (6 marks) Prove that there do not exist two positive integers x and y such that 2-4y2 14. Additional information: you have all known for a long time that there are many solutions to the equation22, where x, y and z are all positive integers. This problem considers a slightly different, but similar looking, type of equations. Hint: use an indirect proof, and start by factoring r2 -4y2

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!

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

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]...

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...

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

lup ] (d) Show how a generating (or "mother") wavelet (x) can spawn a family of "daughter" wavelets jk(x) by simple shifting and scaling operations, and explain the advantages of representing...

\fCPSC 121: Models of Computation Assignment #4, due Wednesday, November 18th , 2015 at 17:00 Each of the following questions asks you to prove a theorem. When the theorem is stated in English, it...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Explain informally the difference between Godel's completeness theorem and his first incompleteness theorem. [8 marks] (b) State the meaning of Hoare triples {P} C {Q} in separation logic. [3 marks]...

Assume that you have an algorithm that can fill 3D triangles with a constant colour. Explain what additional information and additions to the algorithm are required to Gouraud shade the triangles....

We normally consider the gravitational force of the earth on an object of mass m to be given by the constant F = - g mk, but, of course, this is valid only in regions near the earth's surface. Find...

Select true or false for the following statements. 1. Inventory and accounts receivable are both carried at net realizable value. 2.Restricted cash should be reported on the balance sheet as part of...

The budget prepared for the general fund for the current fiscal year included total appropriations of $ 2 , 5 2 0 , 0 0 0 and estimated revenues of $ 2 , 2 5 0 , 0 0 0 . Government - Wide General...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

1. On balance, do you think networking is best thought of as a way to meet interesting people or a way of using people to get what you want?

2. Assuming that, after his reassignment, John might have become more open to suggestions on his behavior, how might you advise him?

3. If you were John and had the benefit of hindsight, how might you have handled the situation differently? How could you use power and organizational politics to gain the respect and cooperation you...