My Math Forum Prove the polynomial f(x)=x^2-q is irreducible in F_p[x]?

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 November 1st, 2015, 09:39 AM #1 Newbie   Joined: Nov 2015 From: Toronto Posts: 2 Thanks: 0 Prove the polynomial f(x)=x^2-q 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^2-q is irreducible in F_p[x].
 November 1st, 2015, 12:09 PM #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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