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

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Start date Nov 1, 2015
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k3232x

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Nov 1, 2015

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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Euge

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MHB

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Nov 1, 2015

Hi k3232x,

Welcome. (Wave) Please show what work you've done or what your thoughts are about this problem. That way, we can assist you better.

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

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

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