Irreducible in Z[x]: (x-a1)(x-a2)....(x-an)+1

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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
 
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That statement isn't true.
 
give anr coutrexmple
 
sayan2009 said:
give anr coutrexmple

(x-1)(x-3)+1=x^2-4x+4=(x-2)^2
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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