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k3232x
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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].
MHB Prove the polynomial f(x)=x^2-q is irreducible in F_p[x]?
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The discussion focuses on proving the irreducibility of the polynomial f(x)=x^2-q in the context of F_p[x], given that p and q are prime numbers with p not being a quadratic residue mod q. A key condition is that pq=-1 mod 4, which plays a crucial role in the proof. Participants encourage sharing any preliminary work or thoughts to facilitate better assistance. The conversation emphasizes collaboration and the importance of understanding the underlying concepts for a successful proof. Engaging with the problem's specifics is essential for clarity and progress.
Hello!
In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way:
I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true?
And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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