• Support PF! Buy your school textbooks, materials and every day products Here!

Irreducible in Z[x]

  • Thread starter sayan2009
  • Start date
  • #1
14
0

Homework Statement



show that the polynomial (x-a1)(x-a2).............(x-an)+1 is irreducible in Z[x],where a1,a2,.....an are distinct odd integers

Homework Equations





The Attempt at a Solution

trying to use eisenstein criterion...but cant
 
Last edited:

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
That statement isn't true.
 
  • #3
14
0
give anr coutrexmple
 
  • #4
283
3
give anr coutrexmple
[tex](x-1)(x-3)+1=x^2-4x+4=(x-2)^2[/tex]
 

Related Threads for: Irreducible in Z[x]

Replies
7
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
10K
Replies
5
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
17
Views
7K
Replies
6
Views
2K
Replies
1
Views
844
Top