Prove there are infinitely many primes by showing that Qn = n! + 1 must have a

Question:

Prove there are infinitely many primes by showing that Qn = n! + 1 must have a prime factor greater than n whenever n is a positive integer.

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

Adapt the proof in the text that there are infinitely many primes to prove that there are infinitely many primes of the form 4k + 3, where k is a nonnegative integer.
Use Dirichlet's theorem, which states there are infinitely many primes in every arithmetic progression ak + b where gcd(a, b) = 1, to show that there are infinitely many primes that have a decimal...
Adapt the proof that there are infinitely many primes (Theorem 3 in Section 4.3) to show that are infinitely many primes in the arithmetic progression 6k + 5, k = 1, 2, . . ..
Describe some practical examples of the single-resource sequencing problem.
Suppose that you are the analyst charged with developing a new system for the university bookstore with which students can order books online and have them delivered to their dorms and off-campus...
Draw a reaction energy diagram for a two-step reaction that has an endothermic first step and an exothermic second step. Label the reactants, transition states, reaction intermediate, activation...
Sports-Related Concussions in Kids Researchers examined all sports-related concussions reported to an emergency room for children ages 5 to 18 in the United States over the course of one year. Table...
For each definition (or portion of a definition) in the first column, select the term that most closely applies. Each term may be used only once or not at all. Definition (or Portion) a. A detailed...
a. What resources are shared among different threads in a multithreaded process? (10 points) b. Describe two differences between user-level and kernel-level threads. In what circumstances is one...
Suppose that a data file contains a sequence of 8-bit characters such that all 256 characters are about equally common: the maximum character frequency is less than twice the minimum character...
Show that an integer is divisible by 9 if and only if the sum of its decimal digits is divisible by 9.
Show that every integer greater than 11 is the sum of two composite integers.
Solve the given differential equation by undetermined coefficients. y'' - 2y'' - 24y = 16 - (x + 2)e 4x
Write a SET client SpellChecker that takes as a commandline argument the name of a file containing a dictionary of words, and then reads strings from standard input and prints any string that is not...
Find a function whose order of growth is larger than any polynomial function, but smaller than any exponential function. Extra credit: Find a program whose running time has that order of growth.
Create a new constructor so that Queue \(r=\) new Queue \((q)\); makes \(r\) a reference to a new and independent copy of the queue \(q\).
Given an array of \(n\) integers, design a linearithmic-time algorithm to determine whether any two of them sum to 0 .
Write a method that takes the first Node in a linked list as its argument and reverses the list, returning the first Node in the result.
The statement of financial position of Euston Ltd as at 31 December 20X9, with corresponding amounts, showed the following: 1. Property, plant and equipment includes the following: 2. An item of...
Use this circle graph to answer following Exercises. 1. What fraction of areas maintained by the National Park Service are designated as National Recreation Areas? 2. What fraction of areas...
Suppose X has a hypergeometric distribution with N = 10, n = 3, and K = 4. Sketch the probability mass function of X.
Determine the cumulative distribution function for X in Exercise 3-88.
A lot of 75 washers contains 5 in which the variability in thickness around the circumference of the washer is unacceptable. A sample of 10 washers is selected at random, without replacement. (a)...
Find the integrating factor for the given 1-order linear non-homogeneous ordinary differential equation. Do not solve the ordinary differential equation. y xdx-xdy-x+dx + dx
[Bush] Consider the following snippet of code. (Assume that input strings, including null terminator, will always fit within the size 255 array.) char* to_upper_case(char* original) { char...
50. Show that if f(x) = a,x" + a-1x+...+x+ ao, a,..., a-1, and a,, are real numbers and where 0, then f(x) is O(x"). an # Big-O, big-Theta, and big-Omega notation can be extended to functions in more...

Prove there are infinitely many primes by showing that Qn = n! + 1 must have a

Question:

Step by Step Answer:

Note that Q n 2 By the Fundamental Theorem of Arithmetic Q n has a p...View the full answer

Discrete Mathematics and Its Applications

Students also viewed these Statistics questions