Show that (x-a1)(x-a2)...(x-an)+1 is irreducible in Z[x]

[sayan2009]

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

 

[Hurkyl]

That statement isn't true.

 

[sayan2009]

give anr coutrexmple

 

[Focus]

give anr coutrexmple

$$(x-1)(x-3)+1=x^2-4x+4=(x-2)^2$$