Question: Prove that there are no solutions in positive integers x and y to the equation x4 + y4 = 625.

Prove that there are no solutions in positive integers x and y to the equation x4 + y4 = 625.

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since 54 625 for there to be positive int... View full answer

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

Document Format (1 attachment)

Word file Icon

923-M-C-M-S (1378).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Reese Castor, owner of Castor Corporation, is located at 1310 Garrick Way, Sun Valley, Arizona, 86029, phone number is 928-555-8842. The federal EIN is 20-1948348, and the state employer...

Q:

A says "We are both knaves" and B says nothing. Exercises 24-31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie,...

Q:

(a) In (one-dimensional) quantum mechanics, the differentiation operator P[f(x)] = f(x) represents the momentum of a particle, while the operator Q[f(x)] = x f(x) of multiplication by the function x...

Q:

Prove that there are 100 consecutive positive integers that are not perfect squares. Is your proof constructive or non-constructive?

Q:

2. (70 points) Are the following statements true or false? If true, prove it and explain which method(s) of proof you have used; if false, disprove it. a. For every positive integer n,(n2+11n+11) is...

Q:

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...

Q:

Find all solutions in positive integers x, y of the equation x3 = 2 + 15 (Hint: Consider that for every integer x, x = 0, 1, 6 (mod7) 3

Q:

5. (a) Give a direct proof of: If x is an odd integer and y is an even integer, then x + y is odd. (b) Give a proof by contradiction of: If n is an odd integer, then n2 is odd. (c) Give an indirect...

Q:

The following questions deal with proofs and recurrence relations. Thanks in advance for you help. Please show step by step solutions. Q. 1 (a) Use a direct proof to show that the product of two odd...

Q:

YORK UNIVERSITY SC/MATH 1019 3.0 D WRITTEN ASSIGNMENT #2 1. (5+5 points) (a) Prove that log(pm + 1) is O(log r) for all m e Et. (b) Give as good a big-O estimate as possible (in terms of the standard...

Q:

Please show all your work The equation x + 2= V3x +10 is of the form x + a = vbx + c , where a, b, and c are all positive integers and b > 1. Using this equation as a model, create your own equation...

Q:

Jose is a 32-year old landscaper living in Pheonix, Arizona. He and his 64-year-old father, Ray, were both diagnosed with metastatic melanoma within two months of one another. Both had their tumors...

Q:

Preparing pro forma income statements with different assumptions Drexel Morris, a successful entrepreneur, is reviewing the results of his first year in business. His accountant delivered the...

Q:

21. In this exercise, you modify one of the Projected Sales applications from this lesson. Use Windows to make a copy of the Sales Solution folder. Rename the copy Sales Solution-Intermediate. Open...

Q:

On January 1 of the current year, Quail Corp., an accrual-basis, calendar-year C corporation, had accumulated earnings and profits (E & P) of $20,000. On December 31 of the current year, Quail Corp....

Q:

What does the message method of Rubys StandardError class do?

Q:

What is the syntactic difference between an HTML widget and its corresponding ASP.NET control?

Q:

Suppose the new product in Example 16.5 has a profit of $5.00 per widget, but the sales projection is of off by 50 percent and the company is able to sell only 500 per day. What is the new break even...

Q:

A spherical rock weighs 30 N in air and 5 N in water. Estimate its terminal velocity as it falls in water (20C).

Q:

The mean and standard deviation of the lifetime of a battery in a portable computer are 3.5 and 1.0 hours, respectively. (a) Approximate the probability that the mean lifetime of 25 batteries exceeds...

Q:

Imagine six points in a plane, no three of which lie on a straight line. In how many ways can the six points be used as vertices to form two triangles? (Hint: Number the points 1 through 6. Call one...

Q:

Show that (k!)! is divisible by k!(k1)!.

Q:

In how many ways can the letters of the word B R O B D I N G N A G I A N be arranged without changing the order of the vowels?

Q:

THX!!! Chapter 5 Financial Planning Exercise 8 Calculating monthly mortgage payments EXHIBIT A Table of Monthly Mortgage Payments (Monthly Payments 5.9 Necessary to Repay a $10,000 Loan) The monthly...

Q:

7 web browser drawbacks

Q:

Suppose that you own 2,800 shares of Nocash Corp. and the company is about to pay a 25% stock dividend. The stock currently sells at $125 per share. a. What will be the number of shares that you hold...