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November 1st, 2015, 08:39 AM  #1 
Newbie Joined: Nov 2015 From: Toronto Posts: 2 Thanks: 0  Prove the polynomial f(x)=x^2q is irreducible in F_p[x]?
If p and q are prime numbers such that p is not a quadratic residue mod q. Show that if pq=1 mod 4 then the polynomial f(x)=x^2q is irreducible in F_p[x].

November 1st, 2015, 11:09 AM  #2 
Senior Member Joined: Dec 2007 Posts: 687 Thanks: 47 
Checking Eisenstein's criterion might be useful: https://en.wikipedia.org/wiki/Eisenstein%27s_criterion 

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fpx, fxx2q, irreducible, polynomial, prove 
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