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November 1st, 2015, 08:39 AM   #1
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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].
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November 1st, 2015, 11:09 AM   #2
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Checking Eisenstein's criterion might be useful:

https://en.wikipedia.org/wiki/Eisenstein%27s_criterion
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