Show that if n2 + 1 is a perfect square, where n is an integer, then n

Question:

Show that if n2 + 1 is a perfect square, where n is an integer, then n is even.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete Mathematics and Its Applications

ISBN: 978-0073383095

7th edition

Authors: Kenneth H. Rosen

See More Books

Question Posted: May 02, 2016 12:27 PM

See More Questions

Show that if a simple graph G has k connected components and these components have n1, n2, . . . , nk vertices, respectively, then the number of edges of G does not exceed C(n,2)
1. Suppose that a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the 2-year period? (The answer is not 7%) 2. Rework...
Prove that there exists a pair of consecutive integers such that one of these integers is a perfect square and the other is a perfect cube.
In Exercises find a power series for the function, centered at c and determine the interval of convergence. f(x) 2 6 - x' C = -2
Interviews should always be conducted as structured interviews." Do you agree with this statement? Why or why not?
Write an equation, using the Friedel-Crafts reaction, for the preparation of
"For many people, being left alone with their thoughts is a most undesirable activity," says a psychologist involved in a study examining reactions to solitude. In the study, 146 college students...
Illegal immigration in the United States is a complex matter, and people have diverse and conflicting ideas on how to best address it. The 2010 GSS contains several questions on this topic. For this...
S Tiger Trade has the following cash transactions for the period. Accounts Cash received from sale of products to customers Cash received from the Bank for long-term loan Cash paid to purchase...
An office building has three floors of rentable space with a single tenant on each floor. The first floor has 20,000 square feet of rentable space and is currently renting for $15 per square foot....
Show that if ac bc (mod m), where a, b, c, and m are integers with m > 2, and d = gcd(m, c), then a b (mod m/d).
Develop a test for divisibility of a positive integer n by 8 based on the binary expansion of n.
A voltmeter with a resistance of 670 k is used to measure the voltage across the 83.0 k resistor in the figure with Problems 79 and 80. What is the voltmeter reading? (a) Redraw the following circuit...
Explain the accounting measurement principles of each of the following: (a) going concern; (b) accruals; (c) consistency; (d) the concept of prudence.
What does the following code fragment print? String string1 = "he11o"; String string2 = string1; string1 = "wor1d"; StdOut.println(string1); Std0ut.println(string2);
Explain how the structure of the balance sheet corresponds to the accounting equation.
What are the main headings to be found in most company balance sheets?
The following technical terms appear for the first time in this Supplement. Check that you know the meaning of each. Profit l Credit purchase Sales revenue l Creditor Cash sale l Trade payable Credit...
The trial balance of Norr Ltd at 31 December 20X9 is as follows: Additional information 1. During the year a motor vehicle purchased on 31 March 20X6 for 8,000 was sold for 3,000. The sale proceeds...
What is removed during each of the three stages of wastewater treatment: primary, secondary, and tertiary? During which state would you expect items to be recovered that were accidentally flushed,...
Three events are shown on the Venn diagram in the following figure:
A digital scale is used that provides weights to the nearest gram. (a) What is the sample space for this experiment? Let A denote the event that a weight exceeds 11 grams, let B denote the event that...
In an injection-molding operation, the length and width, denoted as X and Y, respectively, of each molded part are evaluated. Let A denote the event of 48 = X = 52 centimeters B denote the event of 9...
Lawson Consulting had the following accounts and amounts on December 31. Cash Accounts receivable Equipment Accounts payable Common stock $ 12,000 5,900 Dividends Services revenue. 7,900 Rent expense...
The December 31, 2023, adjusted trial balance of Maritime Manufacturing showed the following information: Single Machinery Accumulated depreciation, machinery1 Office furniture $660,000 312,300...
Peterson Company Beginning of 2020 End of 2020 Direct materials inventory 21,000 23,000 Work-in-process inventory 26,000 25,000 Finished-goods inventory 13,000 20,000 Purchases of direct materials...

Show that if n2 + 1 is a perfect square, where n is an integer, then n

Question:

Step by Step Answer:

We give an indirect proof If n is odd then n 2k 1 for so...View the full answer

Discrete Mathematics and Its Applications

Students also viewed these Statistics questions