Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. show that, for each natural number n, (x ? 1)(x ?

Show that, for each natural number n, (x ? 1)(x ? 2)(x ? 3). . .(x...

60.1K

Verified Solution

Question

Advance Math

Show that, for each natural number n, (x ? 1)(x ? 2)(x ? 3). ..(x ? n) ? 1 is irreducible over Q, the rationals.

Answer & Explanation Solved by verified expert
4.3 Ratings (934 Votes)
We show the irreducibility of the polynomialover by usingthe method of contradictionNote that the polynomial and hence is irreducibleover    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Mechanical Engineering
1.2K views

a)State the ideal cycle most appropriate to the actual operations undergone the modem Diesel engine . b)give...

General Management
1.2K views

Consider the project described in the below Excel a. Construct an Activity-on-Node network for the project. b. Determine...

Physics
1.2K views

31 B Match each item with the correct statement below K U 5 a electric...

Physics
1.2K views

23 A simple pendulum of mass m executes SHM with total energy E If at...

Basic Math
1.2K views

Five pulse rates are randomly selected from a set of measurements. The five pulse rates...

Calculus
1.2K views

Complete the following steps for the given function interval and value of n a Sketch...

Accounting
1.2K views

How distress companies (Manager and Accountants) used accounting discretion for financial health during the pandemic....

Accounting
1.2K views

Shayla Green owns Creative Designs. The trial balance of the firm for January 31, 20X1,...

Accounting
1.2K views

Table 13-3 \table[[\table[[Number of],[Workers]],Output,\table[[Fixed],[Cost]],\table[[Variable],[Cost]],\table[[Total],[Cost]]],[1,0,$50,$0,$50

Accounting
1.2K views

Using the information shown, what is the asset turnover ratio? Net Income...

Accounting
1.2K views

23) Carol is single and has a modified adjusted gross income of $250,000. If she...

Accounting
1.2K views

Which of the following is not a permitted rollover? ...