(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a>1 is a product of distinct primes, show that x^{n}-a is irreducible over Q for all n ≥ 2.

2. Relevant equations

3. The attempt at a solution

I am not really sure how to start this problem. Can anyone point me in the right direction?

I know tests for irreducibility for example Eisensteins Criterion or reduction modulo p but I don't think that these are helpful here?

Thanks for any help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Galois Theory - irreducibility over Q

**Physics Forums | Science Articles, Homework Help, Discussion**